The quantum transition of three coupled Bose–Einstein condensates subjected to an artificial gauge potential is studied in a full quantum description. It shows that as the attractive atomic interaction increases, the system undergoes a transition from non-degenerate to degenerate ground states. This quantum transition point will reach the phase transition point predicted by the mean-field methods when the particle number is infinite, and it can be controlled via the ‘magnetic flux’ ϕ induced by the artificial gauge potential. Specially, when ϕ is odd times of π , around the zero-interaction point, i.e. the phase transition point predicted by the mean-field approach, an interesting quantum phenomenon occurs that the system with finite particles shows different parity effects at two sides of this point. For attractive (repulsive) interaction, the ground state is non-degenerate only when the particle number is a multiple of two (three). The parity effect is due to the symmetric properties of the system at different sides of the transition point. The transition point is then protected by the system symmetry and does not change with the particle numbers.
The quantum transition of three coupled Bose–Einstein condensates subjected to an artificial gauge potential is studied in a full quantum description. It shows that as the attractive atomic interaction increases, the system undergoes a transition from non-degenerate to degenerate ground states. This quantum transition point will reach the phase transition point predicted by the mean-field methods when the particle number is infinite, and it can be controlled via the ‘magnetic flux’ ϕ induced by the artificial gauge potential. Specially, when ϕ is odd times of π , around the zero-interaction point, i.e. the phase transition point predicted by the mean-field approach, an interesting quantum phenomenon occurs that the system with finite particles shows different parity effects at two sides of this point. For attractive (repulsive) interaction, the ground state is non-degenerate only when the particle number is a multiple of two (three). The parity effect is due to the symmetric properties of the system at different sides of the transition point. The transition point is then protected by the system symmetry and does not change with the particle numbers.
Abstract Ultracold atoms with an artificial gauge field provide a powerful platform for studying physical problems in various fields. We investigate the ground state of ultracold atoms in a hexagonal ring lattice with a synthetic magnetic field. The system undergoes a quantum phase transition characterized by degenerate and nondegenerate ground states. The phase transition depends on the atomic interaction and magnetic flux. With the quantum phase transition, a very interesting quantum odd–even parity effect emerges. The parity effects depend on a repulsive or attractive atomic interaction regime.
Spin-orbit-coupled bosons can exhibit rich equilibrium phases at low temperature and in the presence of particle-particle interactions. In the case with a 1D synthetic spin-orbit interaction, it has been observed that the ground state of a Bose gas can be a normal phase, stripe phase, or magnetized phase in different parameter regimes. The magnetized states are doubly degenerate and consist of a many-particle two-state system. In this work, we investigate the nonequilibrium quantum dynamics by switching on a simple one-dimensional optical lattice potential as external perturbation to induce resonant couplings between the magnetized phases, and predict a quantum spin dynamics which cannot be obtained in the single-particle systems. In particular, due to particle-particle interactions, the transition of the Bose condensate from one magnetized phase to the other is forbidden when the external perturbation strength is less than a critical value, and a full transition can occur only when the perturbation exceeds such critical strength. This phenomenon manifests itself a dynamical phase transition, with the order parameter defined by the time-averaged magnetization over an oscillation period, and the critical point behavior being exactly solvable. The thermal fluctuations are also considered in detail. From numerical simulations and exact analytic studies we show that the predicted many-body effects can be well observed with the current experiments.
Quantum mechanically, static or applied gauge fields manifest themselves by directly coupling to a system's phase. Artificial gauge field techniques manipulate the phase of a Bose-Einstein condensate's order parameter, yielding effects present in condensed matter systems subject to magnetic fields, electric fields, or spin-orbit coupling. In this chapter, we explore the impact of these artificial gauge fields on Bose- Einstein condensates and explain the consequences. Several analogues to traditional condensed matter systems are enabled by these techniques, including the Hall effect, superfluid vortex nucleation in systems with artificial magnetic fields, and magnetic-like phase transitions in systems with spin-orbit coupling. Introduction Since the first experiments with Bose-Einstein condensates (BECs), researchers have exploited the universality of physical laws to draw analogies between the behavior of ultracold quantum gases and systems ranging from material to astrophysical. These analogous situations are deliberately engineered, giving cold-atom “quantum simulators” [1] that exhibit behavior either observed or predicted in analogous quantum systems. Superfluidity was one of the first many-body quantum phenomena demonstrated in BECs. For example, several experiments showed superfluid behavior by rapidly rotating the condensates and observing the formation of vortices [2, 3, 4, 5] – quantized point-defects in the BEC's order parameter. In the rotating frame of these experiments, this nucleation of vortices could be understood as the consequence of an artificial magnetic field [6] that arises via the formal equivalence of the rotating-frame Coriolis force and the Lorentz force, which we describe in Section 15.4.1. Together with other measurements, these results proved to be in excellent agreement with the predictions of the Gross-Pitaevskii equation (GPE) [7], a decades-old idealization of superfluid helium. Buoyed by the prospect for studying magnetic field–driven strongly correlated systems using these nearly ideal quantum gases, proposals for alternate techniques to simulate gauge fields were developed. These methods primarily employ an internal state–selective atom–light coupling, where the photon momentum provides the forces necessary to mimic a Lorentz force [8, 9, 10, 11, 12, 13, 14, 15, 16]. The first demonstration of this type of technique used a spatially dependent Ramantransition scheme to effect a magnetic field [17], and experiments demonstrating artificial electric fields [18] and spin-orbit coupling [19, 20, 21, 22, 23, 24] soon followed.
The simplest model of three coupled Bose-Einstein condensates is investigated using a group theoretical method. The stationary solutions are determined using the SU(3) group under the mean-field approximation. This semiclassical analysis, using system symmetries, shows a transition in the dynamics of the system from self trapping to delocalization at a critical value for the coupling between the condensates. The global dynamics are investigated by examination of the stable points, and our analysis shows that the structure of the stable points depends on the ratio of the condensate coupling to the particle-particle interaction, and undergoes bifurcations as this ratio is varied. This semiclassical model is compared to a full quantum treatment, which also displays a dynamical transition. The quantum case has collapse and revival sequences superimposed on the semiclassical dynamics, reflecting the underlying discreteness of the spectrum. Nonzero circular current states are also demonstrated as one of the higher-dimensional effects displayed in this system.
Abstract Spin-tensor-momentum coupling (STMC) induces dramatic change of the single-particle energy spectrum, resulting in rich and novel quantum ground state phases. Here, considering the atomic interactions, the STMC induced Z 2 symmetry breaking of the energy band, the tricritical point and the magnetic phase transitions in trapped STMC Bose–Einstein condensates are presented analytically and numerically. We demonstrate that the ground state momentum and spin tensor are coupled by STMC and the asymmetry of the energy band is persistent in STMC system, resulting in phase transition between magnetized and unmagnetized plane wave phases or between the two unmagnetized plane wave phases. The critical conditions for the phase transitions are obtained analytically, clarifying the physical mechanisms behind the phase transitions. Particularly, a tricritical point is predicted, where different types of energy band merge and the first-order phase transition and the second-order phase transition meet. Interestingly, it is shown that the ground state strongly depends on the external trapping potential, establishing a potential method for manipulating the phase transitions of the system. We provide a theoretical evidence for deep understanding and experimental manipulation of novel quantum phases in STMC systems.
Abstract In the mean-field framework, using variational analysis and numerical simulation, we investigate the effect of anharmonic trap and atomic interaction on the ground-state phases of spin-orbit (SO) coupled Bose–Einstein condensates (BECs) in the harmonic plus quartic potential. Then, the Gaussian wave function is selected to predict the analytical conditions of the phase transition boundary of the SO coupled BECs by using the variational method. We found that the anharmonicity of the external potential induces the SO coupled BECs to undergo a phase transition between the zero-momentum phase and plane-wave phase, which is more pronounced in the cases of weak harmonic potential or strong interspecies interaction. Since the potential energy of the system modified by anharmonicity competes with other energies of the system, the anharmonicity changes the critical SO coupling strength and Raman coupling strength when the phase transition occurs. At the same time, the critical anharmonic coefficients are also affected by interspecies interaction and harmonic potential. Finally, the correctness of the theoretical results is verified by numerical simulation of the Gross-Pitaevskii equation.