Universality in rotating strongly interacting gases

Abstract

We analytically determine the properties of two interacting particles in a harmonic trap subject to a rotation or a uniform synthetic magnetic field, where the spherical symmetry of the relative Hamiltonian is preserved. Thermodynamic quantities such as the entropy and energy are calculated via the second order quantum cluster expansion. We find that in the strongly interacting regime the energy is universal, however the entropy changes as a function of the rotation or synthetic magnetic field strength.PACS numbers: 03.75.Hh, 03.75.Ss, Over the last few years ultracold degenerate gases have attracted much interest due to their controllability and stability. Advances in tight confining harmonic traps and the use of magnetic fields and Feshbach resonances in controlling atomic collisions have made it possible to explore the BCS-BEC crossover [1][2][3]. Difficulties with developing a many-body theory for these systems in the strongly interacting regime using mean-field approximations have motivated the study of few-body problems as a means to gain insight into the many-body problem. Few-body systems with contact interactions are exactly solvable or numericaly tractable [4][5][6][7], particularly in the strongly interacting regime and have been experimentally studied in their own right [8]. The virial expansion of fewbody physics can be used to calculate the thermodynamics of many-body systems [9][10][11] and has been verified experimentally [12].In this work we address the problem of unitary gases subject to a rotation or synthetic magnetic field by solving the two-body problem and finding the virial expansion to second order. This enables us to show that entropy in the presence of a rotation or synthetic magnetic field is not universal, in contrast to the universal character of the total energy.A system subject to a rotation and one subject to a synthetic magnetic field have several similarities. In both systems angular momentum states and time-reversal symmetry are broken. Furthermore, both problems can be described by gauge-dependent Hamiltonians, making it convenient to consider the systems together and to draw comparisons between the two. In ultracold trapped gases the dominant contribution to the low energy behavior is from the two-particle s-wave interactions.To begin the analysis the rotating system is considered first. Specifically, the motion of two particles of mass m in a harmonic trap potential V trap (r) subject to a rotation Ω and a contact interaction potential V int (r 1 − r 2 ) are described by the Hamiltonianwhere r i and p i are the positions and momenta of each particle. Equation (1) can be decoupled in center of mass and relative coordinates, yieldingwhere R = (r 1 + r 2 )/ √ 2 and r = (r 1 − r 2 )/ √ 2 are the center of mass and relative coordinates. We consider the case where the rotation is about the z-axis with frequency Ω z so that Ω = (0, 0, Ω z ). The harmonic trapping potential is chosen to be axially symmetric with transverse and axial frequencies ω ⊥ and ω z , respectively. Using the ...

Coupled-pair approach for strongly interacting trapped fermionic atoms

“…Two-body correlations have been observed to play an important role in these systems [23]. Extensions to more complex systems involving the application of external fields expands the known set of universal relations [24,25].…”

Thermodynamics of rotating quantum matter in the virial expansion

“…Previous work addressing the high-temperature thermodynamics of rotating quantum gases, e.g. in interacting [24,25] as well as noninteracting [26,27] regimes, present different analyses which are complementary to the present work.…”

Two-body quench dynamics of harmonically trapped interacting particles

“…The study of harmonically trapped few-body systems with contact interactions [5][6][7][8][9][10][11] has previously been used to gain insight into the thermodynamic properties of quantum gases [12][13][14][15][16][17][18][19][20][21], particularly in the strongly interacting regime, and have been experimentally studied in their own right [14]. In this paper we focus using the solutions for two interacting atoms in a harmonic trap [5], a regime which is experimentally achievable [2,4], to determine the quench dynamics of such a system.…”