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arXiv:1209.0346 · Physical Review A

Thermodynamics of spin-orbit-coupled Bose-Einstein condensates

Jinling Lian, Yuanwei Zhang, J.-Q. Liang, Jie Ma, Gang Chen, Suotang Jia

Published Dec 17, 2012• 5 citations
arXivHTMLPDF

Abstract

In this paper we develop a quantum field approach to reveal the thermodynamic properties of the Bose-Einstein condensate with equal Rashba and Dresselhaus spin-orbit couplings. In the experimentally feasible regime, the phase transition from the separate phase to the single-minimum phase can be driven well by the tunable temperature. Moreover, the critical temperature, which is independent of the trap frequency, can be derived exactly. At the critical point, the specific heat has a large jump and can be thus regarded as a promising candidate to detect this temperature-driven phase transition. In addition, we obtain the analytical expressions for the specific heat and the entropy in the different phases. In the single-minimum phase, the specific heat and the entropy are governed only by the Rabi frequency. However, in the separate phase with lower temperature, we find that they are determined only by the strength of the spin-orbit coupling. Finally, the effect of the effective atom interaction is also addressed. In the separate phase, this effective atom interaction affects dramatically the thermodynamic properties, including the critical temperature.

DOI
10.1103/physreva.86.063620

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In this paper we develop a quantum field approach to reveal the thermodynamic properties of the Bose-Einstein condensate with equal Rashba and Dresselhaus spin-orbit couplings. In the experimentally feasible regime, the phase transition from the separate phase to the single-minimum phase can be driven well by the tunable temperature. Moreover, the critical temperature, which is independent of the trap frequency, can be derived exactly. At the critical point, the specific heat has a large jump and can be thus regarded as a promising candidate to detect this temperature-driven phase transition. In addition, we obtain the analytical expressions for the specific heat and the entropy in the different phases. In the single-minimum phase, the specific heat and the entropy are governed only by the Rabi frequency. However, in the separate phase with lower temperature, we find that they are determined only by the strength of the spin-orbit coupling. Finally, the effect of the effective atom interaction is also addressed. In the separate phase, this effective atom interaction affects dramatically the thermodynamic properties, including the critical temperature.
In this thesis, we consider the Bose-Einstein condensation of ideal Bose gas in prsence of pseudo spin-orbit coupling. We take equal Rashba and Dresselhaus spin orbit coupling which give rise to degenerate minima at �nite momenta in the ground state eigenvalue and hence form an unconvensional condensate. In this work, we �rst considered the quantum mechanics of this system to calculate energy eigenvalues and the wave function both of which posses a signature of spin orbit coupling. Then we consider the statistical mechanical properties of these systems. In the case of homogeneous system, we �rst calculate the density of states and then the critical temperature of the system. The critical temperature shows a non-analytic point at a particular value of a certain parameter the Raman Coupling which is also known as the point of quantum phase transition in the case of interacting system. Critical temperature at point shows a cusp like structure and drops down to a minimum value at the same point. The critical temperature can be approximated analytically in two di�erent Raman coupling regime before and beyond the critical point from the density of state description. This description can be found by approximating the density of states with that of a free particle with reduced mass in the direction in which the spin orbit coupling takes place. We then consider the magnetization of the system an its variance with the change in the Raman coupling. The magnetization of the condensate vanishes at the same critical point. We next consider the spin orbit coupled Bose gas in a harmonic con�nement. The critical temeperature for this case will show a dip in around the same value of the critical point as in the previous case. But, in this case the drop in the critical temeperature is less sharp and smoothened due to the presense of an harmonic trap. Next we consider the natural extension of the spin bosons to a large spin and we show that it can be exactly mapped to the Dicke model. We can also estimate the critical temperature from this description in a similar fashion.
We obtain the superfluid transition temperature of equal Rashba-Dresselhaus spin-orbit and Rabi coupled Fermi superfluids, from the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensate (BEC) regimes in three dimensions. Spin-orbit coupling enhances the critical temperature in the BEC limit, and can convert a first order phase transition in the presence of Rabi coupling into second order, as a function of the Rabi coupling for fixed interactions. We derive the Ginzburg-Landau equation to sixth power in the superfluid order parameter to describe both first and second order transitions as a function of spin-orbit and Rabi couplings.
The recent realization of synthetic spin-orbit coupling represents an outstanding achievement in the physics of ultracold quantum gases. In this thesis we explore the properties of spin-orbit-coupled Bose-Einstein condensates with equal Rashba and Dresselhaus strengths. These systems present a rich phase diagram, which exhibits a tricritical point separating a single-minimum phase, a spin-polarized plane-wave phase, and a stripe phase. In the stripe phase translational invariance is spontaneously broken, in analogy with supersolids. Spin-orbit coupling also strongly affects the dynamics of the system. In particular, the excitation spectrum exhibits intriguing features, including the suppression of the sound velocity, the emergence of a roton minimum in the plane-wave phase, and the appearance of a double gapless band structure in the stripe phase. Finally, we discuss a combined procedure to make the stripes visible and stable, thus allowing for a direct experimental detection.
We obtain the superfluid transition temperature of equal Rashba-Dresselhaus spin-orbit- and Rabi-coupled Fermi superfluids, from the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensate (BEC) regimes in three dimensions for tunable sss-wave interactions. In the presence of Rabi coupling, we find that spin-orbit coupling enhances (reduces) the critical temperature in the BEC (BCS) limit. For fixed interactions, we show that spin-orbit coupling can convert a first-order (discontinuous) phase transition into a second-order (continuous) phase transition, as a function of Rabi coupling. We derive the Ginzburg-Landau free energy to sixth power in the superfluid order parameter to describe both continuous and discontinuous phase transitions as a function of spin-orbit and Rabi couplings. Lastly, we develop a time-dependent Ginzburg-Landau fluctuation theory for an arbitrary mixture of Rashba and Dresselhaus spin-orbit couplings at any interaction strength.
We study the role of coupling parameters on the ground state phases of spin-orbit coupled Bose-Einstein condensates with an equal combination of Rashba and Dresselhaus coupling strength with Rabi mixing using quasi-one-dimensional coupled Gross-Pitaevskii equations. By considering weak repulsive inter- and intra-species interactions between the condensate atoms, we investigate the contribution of spin-orbit and Rabi coupling parameters on the phases. We find that for a finite Rabi coupling strength, the system undergoes a phase transition from double plane-wave phase to stripe wave phase at a critical spin-orbit coupling strength.
The recent realization of synthetic spin-orbit coupling represents an outstanding achievement in the physics of ultracold quantum gases. In this review we explore the properties of a spin-orbit-coupled Bose-Einstein condensate with equal Rashba and Dresselhaus strengths. This system presents a rich phase diagram, which exhibits a tricritical point separating a zero-momentum phase, a spin-polarized plane-wave phase, and a stripe phase. In the stripe phase translational invariance is spontaneously broken, in analogy with supersolids. Spin-orbit coupling also strongly affects the dynamics of the system. In particular, the excitation spectrum exhibits intriguing features, including the suppression of the sound velocity, the emergence of a roton minimum in the plane-wave phase, and the appearance of a double gapless band structure in the stripe phase. Finally, we discuss a combined procedure to make the stripes visible and stable, thus allowing for a direct experimental detection.