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Fermi liquid-to-Bose condensate crossover in a two-dimensional ultracold gas experiment

Tatiana Barmashova, Kirill Martiyanov, Vasiliy Makhalov, Andrei V. Turlapov

Published Feb 14, 2016• 13 citations
Publisher

Abstract

By controling interparticle interactions, it is possible to transform a fermionic system into a bosonic system and vice versa, while preserving quantum degeneracy. Evidence of such a transformation may be found by monitoring the pressure and interference. The Fermi pressure is an indication of the fermion?ic character of a system, while the interference implies a nonzero order parameter and Bose condensation. Lowering from three to two spatial dimensions introduces new physics and makes the system more difficult to describe due to the increased fluctuations and the reduced applicability of mean field methods. An experiment with a two-dimensional ultracold atomic gas shows a crossover between the Bose and Fermi limits, as evident from the value of pressure and from the interference pattern, and provides data to test models of 2D Fermi and Bose systems, including the most-difficult-to-model strongly coupled systems.

DOI
10.3367/ufne.0186.201602i.0183

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•Aug 12, 2016•1 citation
By controling interparticle interactions, it is possible to transform a fermionic system into a bosonic system and vice versa, while preserving quantum degeneracy. Evidence of such a transformation may be found by monitoring the pressure and interference. The Fermi pressure is an indication of the fermion?ic character of a system, while the interference implies a nonzero order parameter and Bose condensation. Lowering from three to two spatial dimensions introduces new physics and makes the system more difficult to describe due to the increased fluctuations and the reduced applicability of mean field methods. An experiment with a two-dimensional ultracold atomic gas shows a crossover between the Bose and Fermi limits, as evident from the value of pressure and from the interference pattern, and provides data to test models of 2D Fermi and Bose systems, including the most-difficult-to-model strongly coupled systems.
Using an ultracold gas of atoms, we have realized a quasi-two-dimensional Fermi system with widely tunable s-wave interactions nearly in a ground state. Pressure and density are measured. The experiment covers physically different regimes: weakly and strongly attractive Fermi gases and a Bose gas of tightly bound pairs of fermions. In the Fermi regime of weak interactions, the pressure is systematically above a Fermi-liquid-theory prediction, maybe due to mesoscopic effects. In the opposite Bose regime, the pressure agrees with a bosonic mean-field scaling in a range beyond simplest expectations. In the strongly interacting regime, measurements disagree with a purely 2D model. Reported data may serve for sensitive testing of theoretical methods applicable across different quantum physics disciplines.
The physics of many-body systems where particles are restricted to move in two spatial dimensions is challenging and even controversial: on one hand, neither long-range order nor Bose condensation may appear in infinite uniform 2D systems at finite temperature, on the other hand this does not prohibit superfluidity or superconductivity. Moreover, 2D superconductors, such as cuprates, are among the systems with the highest critical temperatures. Ultracold atoms are a platform for studying 2D physics. Unique from other physical systems, quantum statistics may be completely changed in an ultracold gas: an atomic Fermi gas may be smoothly crossed over into a gas of Bose molecules (or dimers) by tuning interatomic interactions. We review recent experiments where such crossover has been demonstrated, as well as critical phenomena in the Fermi-to-Bose crossover. We also present simple theoretical models describing the gas at different points of the crossover and compare the data to these and more advanced models.
We present a theoretical study of the ground state of the BCS-BEC crossover in dilute two-dimensional Fermi gases. While the mean-field theory provides a simple and analytical equation of state, the pressure is equal to that of a noninteracting Fermi gas in the entire BCS-BEC crossover, which is not consistent with the features of a weakly interacting Bose condensate in the BEC limit and a weakly interacting Fermi liquid in the BCS limit. The inadequacy of the two-dimensional mean-field theory indicates that the quantum fluctuations are much more pronounced than those in three dimensions. In this work, we show that the inclusion of the Gaussian quantum fluctuations naturally recovers the above features in both the BEC and the BCS limits. In the BEC limit, the missing logarithmic dependence on the boson chemical potential is recovered by the quantum fluctuations. Near the quantum phase transition from the vacuum to the BEC phase, we compare our equation of state with the known grand canonical equation of state of two-dimensional Bose gases and determine the ratio of the composite boson scattering length aB{a}_{B}aB​ to the fermion scattering length a2D{a}_{2\mathrm{D}}a2D​. We find ${a}_{B}\ensuremath{\simeq}0.56{a}_{2\mathrm{D}}$, in good agreement with the exact four-body calculation. We compare our equation of state in the BCS-BEC crossover with recent results from the quantum Monte Carlo simulations and the experimental measurements and find good agreements.
The quantum mechanical phenomenon of Bose-Einstein condensation appears throughout physics with manifestations ranging from superconductivity in metals to superfluidity in nuclei and neutron stars. In most cases the condensation emerges due to correlations or pairing of fermionic particles. We explore this quantum behavior in a uniquely controllable and clean system consisting of an ultracold gas of atoms. In particular, by tuning the interactions between the fermionic atoms that make up our ultracold gas we can create condensates consisting of pairs of correlated atoms. These experiments introduce the ability to access the intriguing crossover regime where the quantum behavior of fermions becomes intertwined with that of bosons.
The condensation of fermion pairs lies at the heart of superfluidity. However, for strongly correlated systems with reduced dimensionality the mechanisms of pairing and condensation are still not fully understood. In our experiment we use ultracold atoms as a generic model system to study the phase transition from a normal to a condensed phase in a strongly interacting quasi-two-dimensional Fermi gas. Using a novel method, we obtain the in situ pair momentum distribution of the strongly interacting system and observe the emergence of a low-momentum condensate at low temperatures. By tuning temperature and interaction strength, we map out the phase diagram of the quasi-2D BEC-BCS crossover.
Ultracold atoms have become an essential tool in studying condensed matter phenomena. The advantage of atomic physics experiments is that they provide an easily tunable system. This experiment uses the lowest two ground state hyperfine levels of fermionic lithium. Having two different states creates a pseudo-spin-1/2 system and allows us to emulate electronic systems, such as superconductors and crystal lattices. In our experiment, we can control the ratio between these two states resulting in either a spin-balanced or a spin-imbalanced gas. Imposing an imbalance is analogous to applying a magnetic field to a superconductor which causes the electrons in the material to align to the field (thus breaking the electron pairs which cause superconductivity). This motivates us to understand the phases created when a spin-imbalance is created and the effect of changing the atomic interactions. In a 3D system, we find where superfluidity is suppressed throughout the BEC to BCS crossover. Using phase separation as a guide, we probe the dimensional crossover between 1D and 3D. The phase separation in 1D is inverted from that in 3D, which provides a unique characteristic to distinguish between the dimensions. By varying the tunneling between tubes and the atomic interactions in a 2D optical lattice, we control whether the system is 1D, 3D, or in between. Using the properties of a 3D gas as a guide, we directly observe when the gas has crossed over from being dominated by 1D-like behavior to 3D. In this way, we have found a universal value for the dimensional crossover. The 1D-3D crossover paves the way to search for the exotic FFLO (Fulde-Ferrell-Larkin-Ovchinnikov) superconductor. While most superconductors do not coexist with magnetism, the FFLO phase requires large magnetic fields to support its pairing mechanism. Additionally, this phase is more likely to be found in lower dimensional systems. However, at low dimensions, the effect of temperature fluctuations on the phase is destabilizing, but these temperature effects are reduced with higher dimensionality. Thus, the quasi-1D regime is the optimal region of parameter space to find this phase. The search for direct evidence of FFLO continues in this regime.