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Register a new userEntanglement and dynamical phase transition in a spin-orbit-coupled Bose-Einstein condensate
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Characterizing quantum phase transitions through quantum correlations has been deeply developed for a long time, while the connections between dynamical phase transitions (DPTs) and quantum entanglement is not yet well understood. In this work, we show that the time-averaged two-mode entanglement in the spin space reaches a maximal value when it undergoes a DPT induced by external perturbation in a spin-orbit-coupled Bose-Einstein condensate. We employ the von Neumann entropy and a correlation-based entanglement criterion as entanglement measures and find that both of them can infer the existence of DPT. While the von Neumann entropy works only for a pure state at zero temperature and requires state tomography to reconstruct, the experimentally more feasible correlation-based entanglement criterion acts as an excellent proxy for entropic entanglement and can determine the existence of entanglement for a mixed state at finite temperature, making itself an excellent indicator for DPT. Our work provides a deeper understanding about the connection between DPTs and quantum entanglement, and may allow the detection of DPT via entanglement become accessible as the examined criterion is suitable for measuring entanglement.
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Spin-orbit coupled Bose-Einstein condensates (BECs) provide a powerful tool to investigate interesting gauge-field related phenomena. We study the ground state properties of such a system and show that it can be mapped to the well-known Dicke model in quantum optics, which describes the interactions between an ensemble of atoms and an optical field. A central prediction of the Dicke model is a quantum phase transition between a superradiant phase and a normal phase. Here we detect this transition in a spin-orbit coupled BEC by measuring various physical quantities across the phase transition. These quantities include the spin polarization, the relative occupation of the nearly degenerate single particle states, the quantity analogous to the photon field occupation, and the period of a collective oscillation (quadrupole mode). The applicability of the Dicke model to spin-orbit coupled BECs may lead to interesting applications in quantum optics and quantum information science.
Synthetic spin-orbit (SO) coupling, an important ingredient for quantum simulation of many exotic condensed matter physics, has recently attracted considerable attention. The static and dynamic properties of a SO coupled Bose-Einstein condensate (BEC) have been extensively studied in both theory and experiment. Here we numerically investigate the generation and propagation of a textit{dynamical} spin-density wave (SDW) in a SO coupled BEC using a fast moving Gaussian-shaped barrier. We find that the SDW wavelength is sensitive to the barriers velocity while varies slightly with the barriers peak potential or width. We qualitatively explain the generation of SDW by considering a rectangular barrier in a one dimensional system. Our results may motivate future experimental and theoretical investigations of rich dynamics in the SO coupled BEC induced by a moving barrier.
Entanglement is at the core of quantum information processing and may prove essential for quantum speed-up. Inspired by both theoretical and experimental studies of spin-momentum coupling in systems of ultra-cold atoms, we investigate the entanglement between the spin and momentum degrees of freedom of an optically trapped BEC of $^{87}$Rb atoms. We consider entanglement that arises due to the coupling of these degrees of freedom induced by Raman and radio-frequency fields and examine its dependence on the coupling parameters by evaluating von Neumann entropy as well as concurrence as measures of the entanglement attained. Our calculations reveal that under proper experimental conditions significant spin-momentum entanglement can be obtained, with von Neumann entropy of 80% of the maximum attainable value. Our analysis sheds some light on the prospects of using BECs for quantum information applications.
We study the spin squeezing in a spin-1/2 Bose-Einstein condensates (BEC) with Raman induced spin-orbit coupling (SOC). Under the condition of two-photon resonance and weak Raman coupling strength, the system possesses two degenerate ground states, using which we construct an effective two-mode model. The Hamiltonian of the two-mode model takes the form of the one-axis-twisting Hamiltonian which is known to generate spin squeezing. More importantly, we show that the SOC provides a convenient control knob to adjust the spin nonlinearity responsible for spin squeezing. Specifically, the spin nonlinearity strength can be tuned to be comparable to the two-body density-density interaction, hence is much larger than the intrinsic spin-dependent interaction strength in conventional two-component BEC systems such as $^{87}$Rb and $^{23}$Na in the absence of the SOC. We confirm the spin squeezing by carrying out a fully beyond-mean-field numerical calculation using the truncated Wigner method. Additionally, the experimental implementation is also discussed.
A negative effective mass can be realized in quantum systems by engineering the dispersion relation. A powerful method is provided by spin-orbit coupling, which is currently at the center of intense research efforts. Here we measure an expanding spin-orbit coupled Bose-Einstein condensate whose dispersion features a region of negative effective mass. We observe a range of dynamical phenomena, including the breaking of parity and of Galilean covariance, dynamical instabilities, and self-trapping. The experimental findings are reproduced by a single-band Gross-Pitaevskii simulation, demonstrating that the emerging features - shockwaves, soliton trains, self-trapping, etc. - originate from a modified dispersion. Our work also sheds new light on related phenomena in optical lattices, where the underlying periodic structure often complicates their interpretation.
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