Preparation and Highly Sensitive Detection of Ultracold Molecules

(1)

Preparation and Highly Sensitive Detection of Ultracold Molecules

Dissertation

zur Erlangung des akademischen Grades Doktor der Naturwissenschaften

(Dr. rer. nat.) an der

Universit¨at Konstanz Fachbereich Physik Lehrstuhl Prof. Dr. J. Mlynek

AG Prof. A. Peters, Ph.D.

vorgelegt von

Dennis R. Weise

Oktober 2004

(2)

Dissertation der Universität Konstanz Tag der mündlichen Prüfung:

22. Dezember 2004 Referenten:

Prof. A. Peters, Ph.D.

Prof. Dr. E. Scheer

(3)

Abstract

Over the past decade, magnetic trapping of neutral particles has proven to be a very successful method to spatially confine cold samples for precision spectroscopy or the production of degenerate Bose and Fermi gases. It usually relies on optical precooling in an effective two-level system, which is mainly restricted to atoms with a simple electronic structure. Novel cooling schemes now offer the possibility to extend the recent advances of atomic trapping into the field of ultracold molecular gases. These have lately experienced a growing interest due to many properties not available with atoms.

This thesis establishes concepts and technology for a new experiment to col- lisionally cool and capture molecules at ultralow temperatures. The approach combines buffer-gas loading with a strong superconducting quadrupole magnet in a specially designed ³He-⁴He dilution refrigerator, thereby providing the op- portunity to work with a great variety of paramagnetic particles. Trap depths of more than 1.6 T are realized with the current magnet. Initial tests of the complete apparatus are performed with atomic chromium, for which diffusion in a ⁴He buffer-gas at temperatures between 200 mK and 1200 mK is observed in the presence of trapping fields.

Oxygen is identiﬁed as a ﬁrst suitable molecular candidate for trapping.

In a preliminary experiment, introduction from room-temperature into a 4.2 K experimental cell is accomplished via capillary injection. For ultra-sensitive detection, the NICE-OHMS technique is implemented at cryogenic temperatures for the ﬁrst time. Using a scanned cavity with a ﬁnesse of∼90 000 and a length of 86 mm, an integrated detection sensitivity of 8.8×10⁻⁹/√

Hz is achieved, corresponding to a minimum detectable absorption coeﬃcient of 1.02×10⁻⁸/cm at 10 ms integration time. The work presented here thus provides a basis for precision studies on trapped samples of oxygen and many other molecules as well.

(4)

(5)

Acknowledgments

So many people have contributed to the work presented here that it is very likely to miss some in retrospect. Thus, just to be safe, I would before all like to express my gratitude to those who may be concerned.

First appreciation then deserve my thesis advisors J¨urgen Mlynek and Achim Peters, who set an inspiring stage for the experiment. It has been ﬁnancially supported by the DFG Forschergruppe Quantengase and the Optik Zentrum Konstanz. As part of the latter, I am particular grateful to Georg Maret and Alfred Leitenstorfer for providing continuity.

It is also a great pleasure to thank the Kurt-Alten-Stiftung, which has af- forded a three-month stay at Harvard University for technology transfer. Here, John Doyle’s group welcomed me with an impressive openness and friendliness.

Special acknowledgments go to Rob deCarvalho, Jonathan Weinstein, and Dima Egorov for sharing their invaluable buﬀer-gas experience with me. Our experiment wouldn’t have come very far without it. Bretislav Friedrich has been a knowledgable theoretical advisor, whom I would like to explicitly thank for the enlightening discussions on molecular oxygen.

Over the whole time, it was great to have Oliver Vogelsang as a companion on the experiment. Not many people would have kept teamwork so pleasant in the diﬃcult startup phase. Contributions of all other persons working on the experiment are also much appreciated. These include our Diploma student Robert Hauschild, Sergei Orlov, Jo Bellanca, Andrej Grimm, as well as Michael Stoll and Joost Bakker, who are continuing the work in Berlin. Joost’s tremendous proof-reading commitment has put me deep into his debt.

For making the cavity enhanced spectroscopy experiment possible by lending us their diode laser, I would like to thank Stephan Schiller and Ulf Fr¨ohlich.

Markus Oberthaler’s group needs to be acknowledged not only for dispensing their wavemeter over considerable periods of time, but also for their continuous cooperation in general. This is especially true for the BEC guys Michael Albiez, Thomas Anker, Bernd Eiermann, and Matthias Taglieber. Many other people have contributed to making days and nights on P8 really tolerable, including Harald Schnitzler, Holger Müller, Claus Braxmaier, Andreas Hecker, Hauke Hansen, Evgeny Kovalchuk, and Sven Herrmann. Each of them had his own influence on this work. Of note is moreover the effort of Stefanie Eiden, who reanalyzed our titanium for making sure we had the right alloy.

(6)

I am very thankful to Stefan Eggert, who played an essential role in bringing the involved electronic side of the experiment to life. He taught me much of what I now know about analog devices. Stefan Hahn has been of help in many ways, may it be due to his knowledge in mechanics or his almost famous university- wide connections. For handling annoying paper work and being a considerate contact person for small and not-so-small issues, I wish to thank our secretary Ute Hentzen.

The service of many university facilities has severely been stressed in the course of this work. Thanks go in particular to the liquid helium team with Hartmut G¨orig and Ralf Sieber, the procuring department with Gabriele Sims, as well as to the scientiﬁc machine shop. It made impossible designs possible, and the amazing job of Gerhard Jauch on the magnet titanium structure is legendary.

Finally but most, I would like to sincerely thank my ﬁanc´ee Sonia and my parents. The value of their continuing love and support for me in all the time is beyond words.

Dennis Weise

(7)

List of Figures

1.1 Principle of laser cooling . . . 2

1.2 Status of worldwide atomic trapping . . . 4

2.1 Basic setup for buﬀer-gas loaded magnetic traps . . . 14

2.2 Extended vapor pressure curves for ³He and ⁴He . . . 18

2.3 Temperature dependent number densities for ³He and ⁴He . . . . 19

2.4 Number of collisions for thermalization with the buﬀer-gas . . . . 20

2.5 Ideal temperatures for buﬀer-gas loading . . . 21

2.6 Inﬂuence of the collision cross section on thermalization . . . 22

2.7 Coil conﬁguration in a quadrupole trap . . . 25

2.8 Qualitative ﬁeld distribution in a quadrupole magnet . . . 27

2.9 Trapping potential and number density in a quadrupole trap . . 29

2.10 Typical spatial distribution of thermal loss . . . 31

2.11 Many-body loss in magnetic traps . . . 34

3.1 Main parts of the original dilution refrigerator . . . 38

3.2 Dilution refrigerator picture gallery . . . 39

3.3 Measured helium consumption in the upper dewar . . . 41

3.4 Layout of the retroﬁtted cryostat . . . 42

3.5 Expected magnetic ﬁeld . . . 44

3.6 Magnetic ﬁeld at prominent positions . . . 45

3.7 Exploded magnet mandrel structure . . . 46

3.8 Evolution of the superconducting magnet . . . 47

3.9 Finite element analysis results . . . 48

3.10 Typical magnetic ﬁeld ramp . . . 49

3.11 Experimental ﬁeld values . . . 50

3.12 OFHC copper cell as used for the chromium experiments . . . . 52

3.13 Metal-free G10 experimental cell . . . 53

4.1 Normalized lineshape functions . . . 56

4.2 Particle with arbitrary orientation of the quantization axis . . . . 57

4.3 Absorption and dispersion in a gas . . . 64

4.4 Distribution of absorption in a quadrupole trap . . . 67 v

(12)

vi LIST OF FIGURES

5.1 Electronic structure of atomic chromium . . . 70

5.2 Setup for room-temperature ablation tests . . . 73

5.3 Typical room-temperature ablation signal . . . 74

5.4 Overview of the complete chromium buﬀer-gas loading setup . . 75

5.5 Eddy current heating of the copper cell . . . 77

5.6 Temporal behavior of the cell temperature after ablation for increasing pulse energies . . . 78

5.7 Ablation-induced cell heating . . . 79

5.8 Ablation signals for various initial cell temperatures . . . 80

5.9 Ablation signal at 40 A and a cell temperature of 921 mK . . . . 81

5.10 Peak absorption and sample lifetime at various trap depths . . . 82

5.11 Cross sections for ultracold ⁴He-Cr collisions . . . 83

6.1 Ground-state Zeeman levels of¹⁶O¹⁸O . . . 86

6.2 Vapor pressure curve of molecular oxygen . . . 87

6.3 Number densities at vapor pressure for molecular oxygen . . . 88

6.4 Lower lying valence electronic states of O₂ . . . 90

6.5 A-Band line intensities at diﬀerent temperatures . . . 92

7.1 Optical resonator schematic . . . 96

7.2 Transmission and reﬂection through a cavity . . . 98

7.3 Demonstration of impedance matching in high-ﬁnesse cavities . . 100

7.4 Cavity ﬁeld decay at diﬀerent switching times . . . 101

7.5 Power buildup in a scanned resonator . . . 102

7.6 Distance from the TEM₀₀ to the closest higher order mode . . . 104

7.7 Dependence of cavity transmission on sample absorption . . . 108

7.8 Ideal operation range for cavities with given mirror reﬂectivities . 109 7.9 Optical setup for cavity-enhanced absorption spectroscopy . . . . 110

7.10 Reﬂected intensity from the scanned cavity . . . 111

7.11 Schematic overview of the lock electronics . . . 112

7.12 Generated error signal . . . 113

7.13 Raw oscilloscope traces at 89 mbar oxygen pressure . . . 114

7.14 Cavity transmission at various oxygen pressures . . . 116

7.15 Derivation of lineshape parameters . . . 117

7.16 Measured pressure broadening on the R7Q8 line . . . 118

7.17 Pressure-dependent absorption coeﬃcients . . . 119

7.18 Signal-to-noise ratio . . . 120

8.1 Standard setup for optical frequency modulation . . . 122

8.2 Gallery of typical heterodyne lineshapes . . . 124

8.3 Dual-frequency modulation error signal . . . 126

8.4 Tolerable deviations from resonance for DFM . . . 127

8.5 Basic setup for the implementation of NICE-OHMS . . . 128

8.6 Emergence of a heterodyne signal from intra-cavity dispersion . . 129

(13)

LIST OF FIGURES vii

8.7 Typical NICE-OHMS signal . . . 130

8.8 Conceptual overview of the complete NICE-OHMS setup . . . . 132

8.9 Layout of the LHe cryostat containing the NICE-OHMS cell . . . 134

8.10 Close-up of the lower cryostat with experimental cell . . . 135

8.11 NICE-OHMS experimental cell . . . 136

8.12 Temperature dependence of the resistive capillary heater . . . 137

8.13 NICE-OHMS optical setup – part 1 . . . 138

8.14 NICE-OHMS optical setup – part 2 . . . 139

8.15 Linewidth and drift of the Ti:Sapphire laser . . . 140

8.16 Frequency tuning of the Ti:Sapph via the external port . . . 141

8.17 Demonstration of power stabilization in a 10 GHz laser scan . . . 142

8.18 Resonator design . . . 143

8.19 Determination of the cavity ﬁnesse . . . 144

8.20 Error signal generation and processing for laser-cavity locking . . 145

8.21 Experimental error signal and mode spectrum . . . 146

8.22 NICE-OHMS modulation and signal generation . . . 147

8.23 NICE-OHMS modulation index calibration . . . 148

8.24 FSR tracking module . . . 149

8.25 FSR tracking error signal . . . 150

8.26 Piezo response with decreasing temperature . . . 151

8.27 Measured piezo hysteresis at 295 K and 4.2 K . . . 152

8.28 Experimental NICE-OHMS curves at 295 K and 77 K . . . 153

8.29 DC cavity transmission . . . 154

8.30 Relative line intensities at 295 K and 77 K . . . 155

8.31 Demonstration of NICE-OHMS scanning at 4.2 K . . . 156

8.32 Microscopy images of the output coupler after 4.2 K operation . . 157

8.33 Experimental NICE-OHMS signals at increasing input power . . 158

8.34 NICE-OHMS signal amplitude as a function of input power . . . 159

8.35 Experimental signal-to-noise ratio for NICE-OHMS detection . . 160

8.36 Limiting baseline . . . 160

8.37 Observation of RF interferences at 1.734 GHz . . . 161

A.1 Helium gas handling overview . . . 167

B.1 Squared Clebsch-Gordan coeﬃcients of atomic chromium . . . . 170

C.1 Second harmonic generation of 425 nm laser light . . . 172

C.2 Cavity locking scheme . . . 173

C.3 Frequency response of the cavity piezo . . . 174

C.4 Experimental phasematching curve for SHG of 425 nm light . . . 175

C.5 Output power at 425 nm . . . 176

C.6 Fast frequency sweeping capabilities of the frequency doubler . . 177

D.1 Fit to HITRAN partition sum values for O2 . . . 180

(14)

viii LIST OF FIGURES E.1 Electronic layout of the AOM driver . . . 184 E.2 Electronic layout of the EOM driver . . . 185 E.3 Self-made mechanical RF phase shifter . . . 186

(15)

List of Tables

1.1 Characteristic properties of established trap types . . . 7

1.2 Selected paramagnetic molecules . . . 11

2.1 Coeﬃcients for the He vapor pressure according to the ITS-90 . . 17

2.2 Constants for the He vapor pressure approximation with (2.2) . . 18

3.1 Conﬁguration of the quadrupole coils . . . 43

3.2 Measured mechanical properties of the Ti-5Al-2.5Sn alloy . . . . 47

3.3 Thermal properties of selected materials at 200 mK . . . 51

5.1 Stable isotopes of atomic chromium . . . 69

6.1 Stable oxygen isotopes . . . 84

6.2 Properties of selected oxygen isotopomers . . . 85

6.3 Coeﬃcients for the O2 vapor pressure curve . . . 88

6.4 Classiﬁcation of b¹Σ⁺_g ← X³Σ⁻_g transitions in molecular oxygen . 91 6.5 Strongest oxygen lines in diﬀerent temperature regimes . . . 93

7.1 Good cavity lengths for R1 =R2= 1 m . . . 105

B.1 Energy levels of atomic chromium up to the z⁷P state . . . 168

B.2 Isotopic shifts of the chromium bosons with respect to ⁵²Cr . . . 169

D.1 Spectral line intensities for ¹⁶O2 around the A-Band center . . . 182 D.2 Self-broadening parameters for¹⁶O₂ around the A-Band center . 183

ix

(16)

(17)

Chapter 1

Introduction

Since the development of laser cooling in the 1970s, the field of atomic and molecular physics has experienced a remarkable revival. Laser cooling had orig- inally been suggested as a means of improving the precision of spectroscopic studies on atoms [1,2]. These can be considered as comparatively simple, essen- tially closed systems and thus are an ideal testing ground for new, fundamental theories. As part of a gas-phase sample, however, their individual properties are usually obscured by numerous statistical effects, resulting from collisions with other atoms or the large spread of their velocities, for instance. The influence of these can be reduced by cooling the ensemble and decoupling it from the environment, thereby providing well-defined conditions for a meaningful analysis of their inner structure or interactions. Holding the particles in place at the same time allows for long interaction times and thus high sensitivity. Over the past decades, these ideas have led to a quest for new techniques to not only cool, but also spatially confine dilute clouds of atoms as well as molecules.

The growing sophistication in manipulating the motional degrees of freedom in gas-phase ensembles has not only pushed laser spectroscopy into a regime of unprecedented precision. It has also opened up a totally new research ﬁeld based upon the rich physics of interactions between ultracold particles. When their de Broglie waves start to overlap with decreasing temperature and increasing phase space density, macroscopic signatures of quantum phenomena become visible. In 1995, this was impressively demonstrated by three independent research groups with the ﬁrst observation of Bose-Einstein-Condensation (BEC) [3–5], a phase transition to a new state of matter that had already been predicted in 1925.

These pioneering experiments, awarded with a Nobel prize in 2001, were quickly followed up by further milestones, such as the achievement of Fermi degeneracy in atomic vapors [6], the realization of atom lasers [7–10], and the demonstration of nonlinear atom optics [11].

Today, quantum systems with increasing complexity can be engineered with extensive control over the internal states. However, most of the work is still restricted to the use of atoms, as a general cooling mechanism for molecules

1

(18)

2 INTRODUCTION

~!₀ ~!

excited state

ground state

Figure 1.1: Principle of laser cooling. The light frequency of the incident photons is tuned slightly below an atomic resonance, so that the Doppler effect supports the absorption of photons from a direction opposing the atom’s motion. As the subsequent spontaneous emission is distributed isotropically, the associated recoil on the atom averages out over a large number of cycles. This results in a net deceleration of the atom against the incoming laser light. The process is only efficient for species with a strong transition in an effective two-level system, in which the excited state rapidly decays back to the original ground state to be ready for the next absorption.

has been lacking until recently. Laser cooling is not applicable here, since it relies on repetitive momentum transfer from photons in an absorption process, which is only eﬃcient in cycling transitions (Figure 1.1). These are not found in molecules with their more complex electronic structure, so that temperatures down to 1 K for spectroscopy have so far mainly been accessible in the moving frame of molecular beams [12] or by embedding the molecules in liquid helium droplets [13] or a matrix of a cold carrier gas, where they cannot be regarded as unperturbed.

Although even atomic systems still oﬀer a lot of open terrain for further experiments (Figure 1.2), ultracold molecules are currently moving more and more into the focus of research. Their additional internal degrees of freedom, possibly permanent electric and magnetic multipole moments, and other properties not available in atoms promise a number of new prospects for trapped molecular gases, among which some of the most appealing are:

High resolution spectroscopy

The precision of molecular spectroscopy will certainly benefit from the reduced Doppler broadening and long interaction times available in trapped molecular samples. While this will in the first place improve the theoretical understanding of molecular structure, it should also have an immediate impact on fundamental research concerning the following fields:

Clocks Forbidden transitions in certain molecules oﬀer natural line- widths far below 1 Hz ideally suited for the establishment of new frequency standards. Taking advantage of these lines requires extremely low temperatures and pressures, i. e. ultracold dilute gases.

Testing the foundations of physics Precision spectroscopy on molecules can complement experiments at huge particle collider facilities like

(19)

3 CERN or SLAC looking for physics beyond the Standard Model. This includes tests of the symmetrization postulate with homonuclear molecules [14], CP violation in chiral molecules [15] or the time dependence of fundamental constants. Particular attention has recently been directed towards the search for an electric dipole moment (EDM) of elementary particles, which would indicate a possible violation of time reversal symmetry. Here, polar molecules can serve to boost the attainable level of sensitivity by the signiﬁcant internal enhancement of a moderate, externally applied ﬁeld. First results for the electron have been obtained with YbF [16] and PbO [17, 18].

Degenerate molecular Bose and Fermi gases

In degenerate Bose and Fermi gases, a macroscopic part of the particle ensemble occupies the absolute quantum mechanical ground state. When going to species with an increasing number of internal degrees of freedom, this situation should become harder to realize, as decoherence eﬀects gain more inﬂuence. Molecules of growing complexity might serve to probe this regime. The resulting quantum gases are expected to show special properties as a consequence of the rich rotational-vibrational structure, non-spherical symmetry of the constituents, and unusual interactions [19].

In a Fermi gas of polar molecules, for instance, the long range dipole-dipole force should give rise to a superﬂuid phase transition quite analogous to BCS pairing in solids [20].

Ultracold chemistry and coherent control

Collisions at ultralow temperatures allow fundamental insight into many aspects of particle interactions and thus occupy a position at the inter- section of several disciplines like chemistry, chemical physics, and con- densed matter physics. Traps oﬀer an ideal environment to not only study molecule formation, as already demonstrated with photoassociation spectroscopy [21–24], but also chemical reactions of molecules in unprecedented detail [25]. These might be guided using externally applied ﬁelds [26].

Particularly appealing appears the possibility of investigating overlapping quantum degenerate systems of diﬀerent species with coherent control over the available degrees of freedom [27]. The perspective of initiating chemical reactions between matter waves has already cultivated the term superchemistry [28].

Quantum Computing

Much more than atoms, molecules provide the conditions needed to realize the complex entangled systems required for large scale quantum computing. Aligned molecular dipoles in a 1D array could for instance serve as qubits, which are coupled via the electric dipole-dipole interaction [29].

(20)

4 INTRODUCTION

Li

3

ü ü

Stable boson

BEC has been realized

ü

Quasi-electrostatic trapping should be possible (®0¸10^-23cm³) Optical dipole trap has been realized

Stable fermion

Degenerate Fermi-Gas has been realized

ü ü

Ground state can be magnetically trapped (¹¸1¹_B) Ground state has been magnetically trapped

MOT has been realized

H

1 2He

Li

3 4Be 5B 6C 7N 8O 9F 10Ne

Na

11 12Mg 13Al 14Si 15P 16S 17Cl 18Ar

K

19 20Ca 21Sc 22Ti 23V 24Cr 25Mn 27Co 28Ni 29Cu 30Zn 31Ga 32Ge 33As 34Se 35Br 36Kr

Rb

37 38Sr 39Y 40Zr 41Nb 42Mo43Tc 44Ru 45Rh 46Pd 47Ag 48Cd 49In 50Sn 51Sb 52Te 53I 54Xe

Cs

55 56Ba 72Hf 73Ta 74W 75Re 76Os 77Ir 78Pt 79Au 80Hg 81Tl 82Pb 83Bi 84Po 85At 86Rn

Fr

87 88Ra

Fe

26

La

57

ü ü ü ü

ü ü

ü ü ü

Ce

58 59Pr 60Nd 61Pm62Sm63Eu 64Gd 65Tb 66Dy 67Ho 68Er 69Tm70Yb 71Lu ü ü

ü ü

ü

ü ü ü

ü

*

ü

Figure 1.2:Status of worldwide atomic trapping. While the majority of the elements in the periodic table can be magnetically trapped in the ground state, this has only been realized for a few. The star∗ indicates experiments with metastable atoms.

The question of how to prepare dilute samples of ultracold molecules and ac- complish a wall-free conﬁnement of their motion in all three dimensions remains under debate. A short overview of established cooling and trapping schemes will be given in the following, and the applicability of the competing techniques to molecular species will be discussed.

1.1 Cooling and trapping techniques

Trapping in general arises from a conservative ﬁeld in which the individual particles lose kinetic and gain potential energy when they move away from the trap center. The depth of the trapping potential deﬁnes an energy limit above

(21)

COOLING AND TRAPPING TECHNIQUES 5 which particles will be able to escape from the trap. Therefore, loading of the trap requires a dissipative mechanism that cools the injected particles in the trapping region to translational energies below the trap depth. As the eﬃciency of the loading scheme thus has to be chosen to match the capabilities of the trapping technique, alternatives for the latter will be introduced ﬁrst.

1.1.1 Trap types

Depending on its individual properties, a suitable trapping mechanism can be found for virtually any given particle. Not all of them provide conditions where the minute eﬀects of quantum mechanics become visible, though. The strong Coulomb repulsion in ion traps, for example, dominates all other interactions and limits the obtainable particle number and density in the trap. To allow for high phase space densities and avoid mutual perturbations, the trapped particles should thus be neutral and preferably in the ground state. According trapping schemes typically rely on some form of electromagnetic forces in static or time-varying ﬁelds:

Magnetostatic trap

All paramagnetic particles can in principle be trapped in a local minimum of a static magnetic ﬁeld via the Zeeman eﬀect. This should thus be possible for about 64 % of the stable elements in the ground state (see Figure 1.2), as well as for countless small and large molecules (Table 1.2).

The trapping ﬁeld usually is generated by a suitable combination of coils carrying a constant current. Many conﬁgurations have been demonstrated so far, and trap depths exceeding E/k_B= 1 K are attainable [30].

Electrostatic trap

In analogy to magnetostatic trapping, static electric fields can couple to permanent electric dipole moments to provide confinement via the Stark effect. The lack of such a dipole moment in ground state atoms restricts their use to the trapping of dipolar molecules, though. Here, trap depths of order 500 mK have already been realized [31].

Optical dipole trap

Any polarizable particle can in principle be confined in an optical dipole trap through the ac Stark effect. It relies oninduced dipole moments from laser light tuned far beyond any resonances. In the case of a so-called FORT (Far-Off Resonance Trap), the trap depth still depends slightly on the laser frequency. When the detuning gets even larger, the situation simplifies and the light field can be regarded as a quasi-static electric field polarizing the particle. Under appropriate conditions, the trapping mechanism of such a QUEST (Quasi-Electrostatic Trap) is conservative and independent of the particular sub-level of the electronic ground state.

(22)

6 INTRODUCTION A great variety of diﬀerent particles, and molecules in particular [32], can thus be trapped in the ground state with just one apparatus, even at the same time. Moreover, the use of lasers allows the realization of virtually any trapping geometry.

Optical dipole traps have become feasible with the commercial availabil- ity of continuous-wave lasers oﬀering output powers of 100 W or more.

Particularly well suited for QUESTs are CO2 lasers at 10.6m with output powers in the kilowatt range. Due to the generally low polarizability of most particles, focusing these lasers to spot sizes around 100m still creates rather shallow traps with depths below 1 mK [33].

Microwave trap

Similar to optical dipole traps, microwave traps use ac coupling of permanent or induced dipole moments to a standing-wave electromagnetic field in a cavity for confinement. A suitable interaction can be established both via electric and magnetic dipole forces here. The advantage of all ac schemes is the possibility to trap the absolute ground state in a free-space field maximum, which avoids decay to lower lying untrapped states by spin flip collisions.

Microwave trapping has first been demonstrated for cesium atoms on a ground state magnetic hyperfine transition [34]. A comparatively low trap depth of 0.1 mK was achieved. By using polar molecules, significantly higher values above 1 K should be feasible [35].

Due to its non-conservative nature, a rather special position among the diﬀerent trapping techniques is occupied by the

Magneto-optical trap

A magneto-optical trap (MOT) combines an inhomogeneous magnetic field with optical cooling techniques and exploits radiative selection rules to drive particles to the center of the trap. It is thus subject to the same restrictions as already discussed for pure laser cooling and therefore is in general not suited to confine molecules. Since the frequency of the cooling lasers in a given MOT has to be more or less in resonance with a suitable transition, it also cannot be readily used with a variety of different particles.

Still, the trapping principle is both universal and simple, so that MOTs have been widely used since their ﬁrst demonstration in 1987 [36]. The main advantage of MOTs clearly is their capability to capture atoms from a room temperature vapor. With the exploitation of sub-Doppler cooling techniques, ﬁnal temperatures can be as low as 10K, at characteristic particle densities around 10¹⁰/cm³.

(23)

COOLING AND TRAPPING TECHNIQUES 7

Trap Type Trap Depth Traps Atoms Traps Molecules

MOT 300 K

Magnetostatic 1 K

Electrostatic 500 mK

Optical dipole 1 mK

Microwave 0.1 mK - 1 K

Table 1.1: Characteristic properties of established trap types.

The essential properties of the above mentioned trap types are again summarized in Table 1.1.

1.1.2 Loading schemes

Except for a MOT, eﬃcient loading of the traps introduced in the previous section can only be accomplished if the particles entering the trapping region have translational temperatures below 1 K. They ﬁrst have to be brought into the gas phase, however, which often leads to initial ensemble temperatures beyond 1000 K. Various approaches are available to dissipate the excess kinetic energy in such samples:

Radiation pressure cooling

Light forces can be employed in many ways to slow down particles. With counter-propagating laser beams on three perpendicular axes, for instance, laser cooling can be eﬃciently used to severely restrict their motion in all three dimensions. At low enough velocities, the slowing force has a viscous damping character, giving this setup the name optical molasses.

As previously discussed, however, conﬁgurations relying on momentum transfer from resonant absorption and spontaneous emission of photons are only applicable to very few molecular systems.

In contrast, optical cooling by coherent scattering inside an optical resonator does not depend on the particles’ internal structure and is applicable to polarizable atoms as well as molecules [37]. Translational energies corresponding to K temperatures can be achieved here in all three dimensions by coupling the particles to a far-detuned light ﬁeld inside a single standing-wave optical resonator [38].

Sympathetic cooling

The term sympathetic cooling refers to situations where one particular species is cooled through thermal contact with a second, directly cooled species in the gas phase. Since it relies on elastic collisional energy transfer, a prerequisite is the eﬀective absence of state changing inelastic collisions between the involved particles which would otherwise lead to an unacceptable loss rate in the trap. Sympathetic cooling then oﬀers a good

(24)

8 INTRODUCTION alternative for species not amenable to laser cooling techniques. It was ﬁrst demonstrated for ions in 1986 [39], but since has also been used to cool ensembles of neutral particles into the BEC regime [40].

Buﬀer-gas loading

Closely related to sympathetic cooling is buffer-gas loading [41], in which the species of interest is injected into a vapor of cryogenically cooled helium atoms for thermalization via elastic collisions. The use of the inert noble gas in conjunction with cryogenic techniques offers several advan- tages. Inelastic collisions and chemical reactions with the buffer-gas are strongly suppressed, so that buffer-gas loading should be applicable to a great variety of different particles, including rather large molecules. By slightly changing the temperature of the buffer-gas, the helium vapor pressure — and thus the collision rate — can be adjusted over several orders of magnitude. Unlike sympathetic cooling, this also allows to more or less completely remove the buffer-gas from the trapping region once the sample has been cooled sufficiently for confinement in a suitable trap.

Since the volume covered by the buﬀer-gas is relatively large, high initial particle numbers and densities in the trap are possible.

Cryogenic surface thermalization

For completeness it should be mentioned that atomic hydrogen can be loaded into a magnetic trap by thermalization with a superﬂuid helium surface. It presently still constitutes the most eﬃcient loading scheme in terms of the initial number of particles transferred into the trap. While this technique was crucial for the realization of a hydrogen BEC in 1998 [42], the unique binding properties of hydrogen to liquid helium limit its use to this particular species.

Instead of starting with a hot vapor, one can also take advantage of the already high phase space densities found in ensembles generated by a pulsed supersonic expansion from a nozzle. Here, the spread of velocities already corresponds to a temperature suitable for trapping. It is therefore suﬃcient to reduce the high forward velocity of the sample in the laboratory frame as a whole. This may be accomplished with one of the following techniques:

Stark deceleration

Bunches of polar molecules can be efficiently slowed down with time- varying electric fields in a Stark decelerator [43]. It is based on the same principle that is also utilized in electrostatic traps. Molecules possessing an electric dipole moment will exchange kinetic energy for Stark energy upon entering an electric field, if they are in an appropriate quantum state. When the electric field is quickly switched off before the molecules are gone, they will not regain the lost kinetic energy. Multiple pulsed

(25)

COOLING AND TRAPPING TECHNIQUES 9 electric ﬁeld stages can thus be used successively to bring the molecules to a virtual standstill.

Optical dipole force slowing

Although not yet demonstrated, it is conceivable to scoop particles ex- iting a nozzle at right angles with a nonresonant laser beam steered by a scanner. They can then be decelerated on a circular path by gradually reducing the beam’s angular speed [44]. Such a “laser scoop” resembles a moving optical dipole trap and therefore works both for atoms and molecules.

Alternatively, polarizable particles in a pulsed supersonic jet might also be decelerated by using optical dipole forces in a travelling far-oﬀ-resonant optical lattice [45]. According to theoretical predictions, the moving lattice potential can be tailored such that it reﬂects particles in the jet to zero velocity in the laboratory frame while keeping the initial phase space density.

Mechanical slowing

The rapid forward ﬂow of gas emerging from a nozzle can be largely cancelled if the nozzle is moved in a direction opposing the particle ﬂow.

By mounting it on a high-speed rotor, sample temperatures around 10 K have been obtained in the laboratory frame [46]. It is believed that these can be reduced to below 1 K in an optimized apparatus.

An entirely diﬀerent approach for the preparation of cold molecules is to form them directly in the trap from their atomic constituents:

Conversion processes

Here, all required precursor substances are loaded into the trap ﬁrst, so that the trapping mechanism needs to be able to accommodate those as well as the target molecules. All issues concerning the cooling of more complex particles are thereby completely avoided, as long as the production process does not involve an accompanying momentum transfer.

In recent research, a very successful method of inducing the chemical conversion has been photoassociation [47, 48], where laser light excites two adjacent atoms into a vibrationally excited state of a bound molecule.

Bringing these molecules to the vibrational ground state is not straightforward, though, which signiﬁcantly reduces their lifetime and so far pre- vented further progress in this ﬁeld towards large numbers of trapped, stable molecules.

The use of so-calledFeshbach resonancesin swept magnetic ﬁelds has now opened up a new possibility to reversibly create more stable molecules consisting of local pairs from an ultracold atomic quantum gas. Although

(26)

10 INTRODUCTION this process still leads to relatively high vibrational quantum numbers, it has lately permitted the ﬁrst realization of a molecular BEC in thermal equilibrium with Li₂ [49, 50].

1.1.3 Evaporative cooling

The temperature of a sample just loaded into any kind of trap is primarily determined by the loading mechanism and ranges from tens of K to about 1 K. A further reduction of the ensemble temperature in the trap can be obtained by evaporative cooling [51, 52], a powerful technique that is in general also applicable to molecules.

It is based on the idea that a preferential removal of hot particles from a trapped sample will reduce the average energy of the remaining ones, so that a subsequent rethermalization results in a lower temperature. This is quite analogous to hot coffee in a cup, where the most energetic molecules evaporate and thereby cool the remaining coffee. By common experience, only a small fraction of the coffee needs to be evaporated to considerably reduce the temperature of the rest. Similarly, enough particles stay in the trap although some have to be sacrificed in the cooling process. Therefore, evaporative cooling also leads to a significant increase in phase space density, and usually is the method of choice to bring Bose or Fermi gases to the point of degeneracy.

Evaporative cooling can be implemented by continuously lowering the depth of the trap to induce aforced evaporation, which keeps up a constant removal of particles with energies higher than the trap depth. Hot particles can also be selectively removed throughRF evaporation by making use of the field dependent splitting of the particles’ ground state in the trapping potential. As the most energetic particles are also the only ones to reach high field domains and thus are subject to the largest energy shift, their low-field seeking state can resonantly be coupled to an unbound sublevel by radiation at a suitable radio-frequency without affecting the remaining ensemble.

1.2 This work

So far, not many molecules have been trapped at ultralow temperatures. Among the few are the alkali dimers Li2[49,50], Na2 [53], K2 [54], Rb2[55], and Cs2[56], all produced in high vibrational states via Feshbach resonances at translational temperatures below 10K. The only molecules trapped in the electronic as well as the vibrational ground state have been CaH [57] in a buﬀer-gas loaded magnetic trap at 400 mK, as well as Stark decelerated ND3 [31] and OH [58]

in an electrostatic trap at temperatures down to 50 mK. Ultracold He^∗₂ [22], Ca2 [23], and RbCs^∗ [24] have been generated by photoassociation in MOTs without subsequent trapping.

Only little of the fascinating ground of ultracold molecules has thus so far been covered. Given the still enormous potential, a new experiment to cool and

(27)

THIS WORK 11

Radicals RbO CsO

OH CaH YbF MgF BeCl CaCl NO NO₂ NO₃ CH₃

Triplet Molecules

O₂ SO

PH NH

PF NF

NCl S₂ C₃N₂ SiN₂

CH₂ HCCN

High Spin Molecules

VO GdO

MnH CrH

MnF CrF

MnCl CrCu MnO₂ MoN FeF₃ GdF₃

Organic Molecules Ferrihemoglobin

Propargylene Methylpropargylene

Cyanomethylene Diphenylmethylene

C₆H₅

Ferrihemoglobin Complex

Table 1.2: Selected paramagnetic molecules. Species of virtually any size and com- plexity are in principle available for magnetic trapping. Compare [59] for details.

spatially conﬁne molecules in a trap at ultralow temperatures has been started with this thesis. It is based on buﬀer-gas loading, as this technique is currently considered to be among the most versatile and powerful of all discussed loading schemes. Moreover, it represents one of only two alternatives proven to allow the direct trapping of molecules in the stable vibrational ground state and additionally is also applicable to atoms.

Since buﬀer-gas loading typically leads to ensemble temperatures around 1 K, magnetic trapping remains as the method of choice for subsequent three- dimensional conﬁnement of the injected particles (compare Table 1.1). Both are implemented in this work by integrating a strong superconducting quadrupole magnet into a special, purpose-built ³He-⁴He dilution refrigerator. Potential candidates for trapping can thus be picked from the large class of paramagnetic molecules, some of which are listed in Table 1.2.

Apart from their preparation, also the optical detection of ultracold molecular samples is a major challenge, as expected number densities (like in any trap) are relatively small and many molecules lack strong transitions in regions eas- ily accessible by standard laser sources. Besides the establishment of a suitable technological infrastructure, a main goal of this thesis has therefore been the exploration of ultra-sensitive detection schemes compatible with the cryogenic buffer-gas environment. It is important to realize that these should not only serve to verify the presence of the particles of interest, but also must allow a good characterization of the trapped sample in terms of density, temperature etc. Due to the limited optical access and the presence of the buffer-gas, however, standard techniques such as fluorescence or photoionization spectroscopy [60]

cannot be readily used for this purpose. Instead, the ﬁrst cryogenic implementation of the so-called NICE-OHMS technique [61, 62] is presented here as one possible solution to these requirements.

(28)

12 INTRODUCTION This thesis is organized as follows:

Chapter 2starts out with a discussion of the main principles of buﬀer-gas loading and magnetic trapping.

The actual experimental implementation of these techniques is presented inChapter 3. It gives an overview of the newly developed technological infrastructure, which includes the dilution refrigerator, the superconducting quadrupole magnet, and the specialized experimental cell.

Fundamental aspects relevant for the interpretation of absorption spectra from optical sample detection are then theoretically treated inChapter 4. It provides a basis for the discussion of all detection schemes utilized in the course of this work.

Making use of the universality of the applied loading and trapping techniques, preliminary tests of the complete apparatus have been performed with atomic chromium. These are summarized inChapter 5.

In Chapter 6, oxygen O₂ is considered as a promising molecular candidate for buﬀer-gas loading and subsequent magnetic trapping. Various alternatives for its detection in the trap will be discussed.

Setup and results of an initial experiment on the detection of dilute molecular samples are subject of Chapter 7. The potential of cavity-based spectroscopic methods for this purpose is studied here using O₂ as a test species.

To attain a satisfactory detection sensitivity, cavity-based spectroscopy has ﬁnally been combined with frequency modulation for a NICE-OHMS detection of oxygen molecules.Chapter 8is concerned with the details of its experimental realization under realistic cryogenic conditions. Like the previous chapter, it is accompanied by an in-depth theoretical treatment of the technique.

Although most of the conceptual work in this thesis has in the ﬁrst place been aimed at high precision spectroscopic applications on ultracold molecular gases, it should also provide a technological foundation for future research towards molecular quantum gases.

(29)

Chapter 2

Buﬀer-Gas Loading and Magnetic Trapping

Buffer-gas loading in conjunction with magnetic trapping has first been suggested by Doyle and coworkers [63]. It has so far been applied to the atomic species of europium (7µ_B) [64], chromium (6µ_B) [30], and molybdenum (7µ_B) [65]. Molecular calcium monohydride (CaH) with 1µ_B was successfully loaded, but the trap lifetime was limited to about 0.5 s [57]. Much longer lifetimes for species with small magnetic moments are achievable if the buffer-gas is removed sufficiently fast, as recent results indicate [65]. Buffer-gas cooling without trapping has been demonstrated for vanadium monoxide (VO) [66], lead monoxide (PbO) [18] as well as rubidium atoms [67].

In summary, all previous results document that buﬀer-gas loading is in particular suitable to trap the majority of all paramagnetic molecules, which is going to be exploited in the project started with this thesis. To present knowledge, it represents the only further experiment worldwide based on this technique.

Main aspects of the loading and trapping mechanism will be introduced in the following.

2.1 Basic principle

Efficient loading of any trap ideally requires initial translational sample temperatures an order of magnitude lower than the available trap depth. This constraint makes it quite natural to combine magnetic trapping with buffer-gas cooling in a helium vapor. On the one hand, magnetic traps presently provide the highest trap depth of all conservative trapping techniques. Since this still is just of order 1 K, helium on the other hand remains as the only choice for the buffer-gas species, because all other stable substances have negligible vapor pressure at this temperature. From a practical point of view, the necessity of a cryogenic environment for cooling the helium buffer-gas facilitates the use of superconducting magnets, which provide superior field strengths and less power

13

(30)

14 BUFFER-GAS LOADING AND MAGNETIC TRAPPING

sample detection laser ablation

capillary sample injection He buffer-gas thermal link

to cryostat

solid precursor material

magnetic field generating coils

Figure 2.1:Basic setup for buﬀer-gas loaded magnetic traps. Since no metallic material should be used for the cell to avoid eddy current heating when ramping the magnetic ﬁeld, the thermal link to the cryostat cold plate is indicated here with liquid helium.

dissipation.

The basic idea of buﬀer-gas loading is as simple as it is appealing. A typical experimental setup is schematically depicted in Figure 2.1. An experimental cell containing either a³He or⁴He vapor above a liquid phase is thermally attached to a suitable cryostat, usually a³He-⁴He dilution refrigerator. The trapping ﬁeld with a local minimum at the cell center is generated by an anti-Helmholtz magnet or an alternative suitable combination of coils. Prior to sample injection, the cell temperature is raised by heaters to create an adequate number density of helium atoms in the gas phase. This has to be chosen such that the injected

(31)

SAMPLE PRODUCTION 15 particles will thermalize with the helium buffer-gas on their way through the cell before reaching the wall, where they would stick with virtual unity proba- bility and be lost. Once the average particle energy is below the trap depth, the heaters are switched off again and the buffer-gas is extracted from the trapping region through recondensation on the cell wall or additional active pumping.

In contrast to helium, paramagnetic particles in low-field-seeking states will be captured by the magnetic field and thus be held in the cell center. With an appropriate timing, one is left with a large number of thermally isolated trapped particles surrounded by an almost perfect vacuum. Their temperature will ap- proximately equal the buffer-gas temperature at the time of thermalization.

2.2 Sample production

Among the various techniques available to produce a gas-phase sample of the species of interest for subsequent cooling and trapping, laser ablation from a solid precursor material has been found to be particularly suitable for buﬀer-gas loading in the cryogenic environment [68, 69]. Since optical access to the experimental cell is needed anyway for detection, it is straightforward to implement and the method of choice for all metals and some more complex particles.

The precursor substance is usually placed above the trap center slightly beyond the edge of the trapping potential. A laser pulse loosely focused on this target will be partially absorbed and the deposited energy results in melt- ing, evaporation and plasma formation. In a very complex process, all kinds of different neutrals, ions, and compounds will be formed and come off in a hot plume of several hundred degrees Kelvin. Any of the liberated particles in low-field seeking states with a high enough magnetic moment can potentially be trapped.

The physical details of laser ablation are not well-understood, so that the experimental conditions are best optimized by trial and error to maximize the yield and avoid the production of unwanted species. Typical pulse energies in this thesis have been between 10 and 120 mJ for pulse durations around 10 ns at a wavelength of 532 nm. In agreement with previous studies, the exact spot size on the precursor has been found to be uncritical.

An important issue within the context of buﬀer-gas loading is the heating of the precursor lump and the experimental cell through the ablation pulse. To avoid an intolerable increase of the helium vapor temperature and density, this should be kept as low as possible. The thermal contact from the precursor to the cryostat cold plate therefore has to be carefully engineered and the amount of pulse energy converted to heat has to be balanced against the commonly low cooling power in the cryogenic environment.

While laser ablation is well suited for substances whose precursor material is already solid at room-temperature, an alternative for other species has recently been demonstrated with the buﬀer-gas cooling of a beam of rubidium atoms to

(32)

16 BUFFER-GAS LOADING AND MAGNETIC TRAPPING 4.2 K [67]. Apart from extending the range of potential candidates for trapping, the use of atomic and molecular beam sources in combination with buffer-gas loading would also offer further perspectives. By employing the versatile and mature methods available to produce and manipulate gas-phase particles in thermal beams, a particle selection or state preparation prior to loading would become possible, for instance. Moreover, the large attainable fluxes promise relatively high initial particle numbers and densities in the trap.

A third way of introducing particles into the buﬀer-gas cell at cryogenic temperatures is capillary injection, which has been pursued and tested in this thesis. It was demonstrated to temperatures as low as 1.8 K in the ’80s [70]

and should complement laser ablation more or less in the same manner as beam-based methods would. As sketched in Figure 2.1, a capillary connects the experimental cell with a leak-valve port outside the cryostat, from where any room temperature gas could be injected. Resistive heating of the capillary avoids condensation or solidiﬁcation of the gas on its way to the trapping region, which would otherwise possibly plug the line. Care has to be taken to make the heating needs compatible with the stringent thermal restrictions set by the limited cooling capabilities of the employed cryostat.

2.3 Buﬀer-gas loading

After producing a gas-phase sample or injecting it into the experimental cell, the thermalization process with the helium buffer-gas is governed by the helium temperature, its corresponding density and the associated scattering cross sections. It can be influenced by selecting either ³He or ⁴He as the buffer-gas species and setting its vapor pressure. This is controlled during loading of the trap through one of two procedures:

The usual method as described above is referred to as normal loading.

The initial cell temperature is mainly set by the available cooling power and should be as low as possible. Resistive heaters then adjust it from this point according to experimental needs following the discussed procedure.

Cold loadingcan only be used in conjunction with laser ablation. Here, the heat from the ablation pulse itself is used to bring enough helium atoms into the gas phase. No artiﬁcial temperature increase prior to sample production is necessary. The experimental cell is instead continuously cooled, so that the evaporated helium is cryopumped from the trapping region more quickly. Although this is a highly dynamical process, it still results in a successful loading of the trap [41].

An upper limit of the buﬀer-gas number density is usually set close to the op- timum value through the total amount of helium admitted to the experimental cell. Essential parameters will be quantiﬁed next.

(33)

BUFFER-GAS LOADING 17 2.3.1 Helium vapor pressure

Exact knowledge of the helium vapor pressure is mandatory to experimentally control and analyze the thermalization process with the buffer-gas. While other trapping experiments have to adjust the scattering length artificially with external fields, it is much easier to control the scatteringrate via the helium number density to obtain sufficient cooling. Appropriate vapor pressure curves of ³He and ⁴He are well-established through the International Temperature Scale of 1990 (ITS-90). It defines them from 0.65 to 3.2 K for ³He and 1.25 to 5.0 K for

4He by

T(p) = 9 i=0

A_i

ln(p)−B C

_i

, (2.1)

where the constants are given in Table 2.1, T is in Kelvin and p is the vapor pressure in Pascal [71]. An extrapolation to lower temperatures can be obtained from the Clausius-Clapeyron equation. Assuming an ideal gas withpV =νRT and a negligible molar volume of the liquid phase with respect to the gas phase, which both is extremely accurate for helium under these conditions, yields

dp

dT = L(T) RT² p .

With the further approximation of a constant latent heat of evaporation L, this diﬀerential equation is of course solved by the exponential

p(T) =p₀·exp

− L RT

. (2.2)

A rough estimate of the helium vapor pressure for temperatures below the valid- ity range of the ITS-90 can be found by either ﬁtting (2.2) to values calculated from (2.1) or by analytic continuation of (2.1) at the temperature limits. The

3He (0.65 - 3.2 K) ⁴He (1.25 - 2.1768 K) ⁴He (2.1768 - 5.0 K)

A₀ 1.053477 1.392408 3.146631

A₁ 0.980106 0.527153 1.357655

A₂ 0.676380 0.166756 0.413923

A₃ 0.372692 0.050988 0.091159

A₄ 0.151656 0.026514 0.016349

A₅ -0.002263 0.001975 0.001826

A₆ 0.006596 -0.017976 -0.004325

A₇ 0.088966 0.005409 -0.004973

A₈ -0.004770 0.013259 0

A₉ -0.054943 0 0

B 7.3 5.6 10.3

C 4.3 2.9 1.9

Table 2.1:Coeﬃcients for the He vapor pressure according to the ITS-90.

Preparation and Highly Sensitive Detection of Ultracold Molecules