• Abstract and Figures
• Public Full-text

Fluctuations in Quantum Degenerate Fermi Gases Fluctuations in Quantum Degenerate Fermi Gases by Christian Sanner Abstract Ultracold neutral Fermi gases provide a novel platform for the experimental quantum simulation of correlated many-body systems. The study of fluctuations and correla- tions in Fermi gases and the development of appropriate measurement methods are the subject of this thesis. Spatial atom noise analysis performed for expanded clouds of an ideal Fermi gas reveals Pauli suppression of density fluctuations for cold gas samples deep in the quantum degenerate regime. Measuring the level of suppression provides sensitive thermometry at low temperatures. Spin fluctuations and density fluctuations are studied for a two-component gas of strongly interacting fermions along the Bose-Einstein condensate - BCS crossover. This is done by in situ imaging of dispersive speckle patterns. Compressibility and magnetic susceptibility are determined from the measured fluctuations. Speckle imag- ing easily resolves a tenfold suppression of spin fluctuations below shot noise, and can be universally applied to trapped quantum gases. A degenerate Fermi gas is rapidly quenched into the regime of strong effective re- pulsion near a Feshbach resonance. The spin fluctuations are monitored using speckle imaging and, contrary to several theoretical predictions, the samples remain in the paramagnetic phase for an arbitrarily large scattering length. Over a wide range of interaction strengths a rapid decay into bound pairs is observed over times on the order of a few Fermi times, preventing the study of equilibrium phases of strongly repulsive fermions. This suggests that a Fermi gas with strong short-range repulsive interactions does not undergo a ferromagnetic phase transition. December 2012 Acknowledgments Having too much stress in your life? Go visit the zoo! Building 26 floor 2 is a zoo. It is a marvelous zoo, a microcosm of scientific leisure almost completely shielded from all annoyances that normally constrain life. Being one of the shy animals I am very thankful to the zookeeper for letting me hide from visitors, cookie hours, daylight, seminars and other forms of harsh reality. I am thankful to Wolfgang for a lot of other things. MIT is a research institute and not a Zen eldorado, but most of the time it felt like it anyway. This is because of the patience and humility of many people that I had the privilege to work with over the years. Many thanks to all my wonderful colleagues, among them in particular Jit Kee Chin, Dan Miller, Marko Cetina, Ying- mei Liu, Widagdo Setiawan, Aviv Keshet, Edward Su, Ralf Gommers, Yong-il Shin, Wujie Huang and Jonathon Gillen. Thank you also for mostly sharing a passion for terminated photodiodes! Special thanks to Markus Oberthaler and Selim Jochim. Finally I am thankful to Conrad Fischer, Larry Hagman, Friedrich K¨uppersbusch, Paul Pranzo, Saint Bruno of Cologne, Louise Clancy, Jerry Shine, Yuri Gagarin, Mother Teresa, Heiner M¨uller, Heinz Heimsoeth, Richard Slotkin, Justin Pierce, Princess Leia and Luke Skywalker for providing insight beyond imagination. Ahoy! Contents 1 Introduction 7 1.1 Mean values and fluctuations ...................... 8 1.1.1 Why is the physics of fluctuations interesting? ......... 8 1.2 Fluctuations and experiments with cold atoms ............. 9 1.2.1 New ways to probe interesting quantum phases ........ 9 1.2.2 Noise and correlation measurements - The state of the field . 10 1.2.3 A universal approach to noise measurements - Synopsis and outline ............................... 11 2 Theory of fluctuations in Fermi gases 14 2.1 The fluctuation-response relation .................... 14 2.2 Bosons vs. Fermions - Different noise properties ............ 17 2.3 Density fluctuations in a non-interacting Fermi gas .......... 18 2.3.1 Large probe volume limit ..................... 18 2.3.2 Small probe volume limit ..................... 20 2.4 Fluctuations in an interacting Fermi gas ................ 23 2.5 Density fluctuations and light scattering ................ 25 3 Measuring fluctuations in an ideal Fermi gas 27 3.1 Measurements in trap and after ballistic expansion .......... 28 3.2 The experimental procedure ....................... 30 3.2.1 Fermi gas apparatus ....................... 30 3.2.2 Sample preparation ........................ 31 4 3.3 How to count atoms in a box - Experimental challenges and constraints 33 3.3.1 Different imaging methods .................... 33 3.3.2 Atom noise and other noise sources ............... 35 3.3.3 Nonlinear effects and other limitations ............. 42 3.4 The imaging system for noise measurements .............. 46 3.4.1 Overview of the imaging system ................. 47 3.4.2 Detector optimization for noise measurements ......... 50 3.4.3 Further improvement strategies - Coherent vs. incoherent illu- mination .............................. 56 3.4.4 Depth of field considerations . ................. 60 3.5 Data acquisition and analysis ...................... 61 3.5.1 Horizontal statistics vs. vertical stack analysis ......... 62 3.5.2 The vertical noise measurement procedure ........... 64 3.5.3 Scattering cross section calibration ............... 66 3.6 Measurement results and interpretation ................. 68 3.6.1 Comparison of theory and experiment .............. 68 3.6.2 Atom counting contrast saturation ............... 70 3.6.3 Noise in the noise ......................... 71 4 Measuring fluctuations in a strongly interacting Fermi gas 73 4.1 Properties of an interacting two component Fermi gas ......... 74 4.1.1 From elastic collisions to Feshbach resonances ......... 74 4.1.2 A Fermi gas in the unitary limit ................. 75 4.2 In-situ noise measurements - Advantages and challenges ........ 79 4.2.1 A short review of Fourier optics ................. 80 4.2.2 Dispersive imaging ........................ 81 4.2.3 Initial experimental strategy ................... 84 4.3 From laser speckle to speckle imaging .................. 86 4.3.1 Laser speckle ........................... 86 4.3.2 Out-of-focus speckle ....................... 87 4.4 Data acquisition and analysis ...................... 89 4.4.1 Experimental setup and sample preparation .......... 89 4.4.2 Noise extraction and mapping procedure ............ 90 4.4.3 Determination of the superfluid to normal phase boundary . 94 4.5 Results and interpretation ........................ 95 5 Exploring correlations in a repulsively interacting Fermi gas 98 5.1 Ferromagnetic instability of a repulsive Fermi gas ........... 98 5.1.1 The critical interaction strength ................. 100 5.1.2 Pairing instability vs. ferromagnetic instability ......... 101 5.2 Experimental strategy .......................... 102 5.3 Experimental results - Discussion and interpretation .......... 104 5.3.1 Spin fluctuation measurements .................. 104 5.3.2 Pair formation measurements .................. 105 5.3.3 Rate comparison ......................... 107 5.3.4 Temperature considerations ................... 108 5.3.5 Kinetic energy and release energy ................ 109 5.3.6 Time scales for domain growth vs. experimental resolution . 112 5.4 Conclusions ................................ 113 6 Conclusions and outlook 115 A Suppression of Density Fluctuations in a Quantum Degenerate Fermi Gas 117 B Speckle Imaging of Spin Fluctuations in a Strongly Interacting Fermi Gas 122 C Correlations and Pair Formation in a Repulsively Interacting Fermi Gas 127 Chapter 1 Introduction The field of ultracold quantum gases continues to expand. Bose-Einstein condensation of dilute alkali vapors [1, 2] opened up a multitude of research possibilities and led eventually to the experimental study of quantum degenerate Fermi gases [3] and new phases in optical lattices [4]. Particularly in this context it is evident that the expansion of the field is not mere diversification. Instead, cold quantum gases are becoming a model system to investigate universal physics [5] and to address long- standing questions relevant for solid state many-body systems [6]. The experiments described in this thesis follow this concept. Individually they demonstrate fundamental effects of quantum mechanics, reveal pair correlations in a superfluid and attempt to investigate the possibilities for itinerant ferromagnetism in a strongly interacting quantum gas. However, altogether they want to contribute towards the implementation of a quantum simulator for solid state systems. This chapter will provide a motivation and general introduction to fluctuation and correlation experiments with cold atoms. 7 1.1 Mean values and fluctuations 1.1.1 Why is the physics of fluctuations interesting? Every experimentalist is confronted with fluctuations in the quantity of interest. Of- ten these fluctuations have a technical origin, e.g. uncertainties caused by residual mechanical vibrations in a measurement setup, and contribute to the error budget of the experiment. In the absence of technical noise the outcome of a measurement is typically still noisy, but now the noise reflects fundamental properties of the studied system. Measuring the voltage drop across an electrical resistor is a good example. Ini- tially technical noise in the measurement device - for instance an oscilloscope - might be the limiting factor, but eventually one finds that irreducible forms of noise are associated with every resistor. The random thermal motion of the charge carriers in the conductor gives rise to thermal Johnson noise, and for very low currents through the resistor the quantization of charge

Load more

  142

Copy Link