Statistical properties of spectra in harmonically trapped spin–orbit coupled systems

Marchukov, Oleksandr V.; Volosniev, A. G.; Fedorov, D. V.; Jensen, A. S.; Zinner, N. T.

doi:10.1088/0953-4075/47/19/195303

Cited by 16 publications

(22 citation statements)

References 59 publications

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“…The most famous example of this is the existence of a stripe phase that is an equal superposition of two minima in momentum space [40]. The ground state and collective excitations of SOC BECs have been investigated for a large number of different settings, such as homogeneous [40][41][42][43][44][45][46][47][48][49], harmonic [50][51][52][53][54], in the presence of a periodic optical lattice [55][56][57][58][59][60][61][62][63][64][65][66][67][68][69][70][71][72], a double-well [73][74][75], rotation [76][77][78][79][80][81], inside an optical cavity [82][83][84][85][86], and for particles with dipolar interaction …”

Section: Introductionmentioning

confidence: 99%

Properties of spin–orbit-coupled Bose–Einstein condensates

et al. 2016

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The experimental and theoretical research of spin-orbit-coupled ultracold atomic gases has advanced and expanded rapidly in recent years. Here, we review some of the progress that either was pioneered by our own work, has helped to lay the foundation, or has developed new and relevant techniques. After examining the experimental accessibility of all relevant spin-orbit coupling parameters, we discuss the fundamental properties and general applications of spin-orbit-coupled Bose-Einstein condensates (BECs) over a wide range of physical situations. For the harmonically trapped case, we show that the ground state phase transition is a Dicke-type process and that spin-orbit-coupled BECs provide a unique platform to simulate and study the Dicke model and Dicke phase transitions. For a homogeneous BEC, we discuss the collective excitations, which have been observed experimentally using Bragg spectroscopy. They feature a roton-like minimum, the softening of which provides a potential mechanism to understand the ground state phase transition. On the other hand, if the collective dynamics are excited by a sudden quenching of the spin-orbit coupling parameters, we show that the resulting collective dynamics can be related to the famous Zitterbewegung in the relativistic realm. Finally, we discuss the case of a BEC loaded into a periodic optical potential. Here, the spin-orbit coupling generates isolated flat bands within the lowest Bloch bands whereas the nonlinearity of the system leads to dynamical instabilities of these Bloch waves. The experimental verification of this instability illustrates the lack of Galilean invariance in the system.

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Section: Introductionmentioning

confidence: 99%

Properties of spin–orbit-coupled Bose–Einstein condensates

et al. 2016

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“…Note that Refs. [26,27] examined in detail the spectral properties of another 2D quantum system such as anisotropic harmonic oscillator with SOC in terms of the quantum chaos ensembles. However, the results for the harmonic and Coulomb potentials cannot be compared directly since their eigenstates are qualitatively different in terms of spectrum and wave functions.…”

Section: Numerical Results: Non-poissonian Spectral Statisticsmentioning

confidence: 99%

Energy-level repulsion by spin-orbit coupling in two-dimensional Rydberg excitons

et al. 2018

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We study the effects of Rashba spin-orbit coupling on two-dimensional Rydberg exciton systems. Using analytical and numerical arguments we demonstrate that this coupling considerably modifies the wave functions and leads to a level repulsion that results in a deviation from the Poissonian statistics of the adjacent level distance distribution. This signifies the crossover to non-integrability of the system and hints on the possibility of quantum chaos emerging. Such a behavior strongly differs from the classical realization, where spin-orbit coupling produces highly entangled, chaotic electron trajectories in an exciton. We also calculate the oscillator strengths and show that randomization appears in the transitions between states with different total momenta.

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“…The effect of deforming the trap was considered in Ref. [27], which results in a breaking of the cylindrical symmetry of the system. In our case, the time-reversal symmetry is preserved and, in order to distinguish between the pair of degenerate states, we label them with A and B, respectively, for a given energy E sp .…”

Section: The Single-particle Systemmentioning

confidence: 99%

Spin-orbit-coupled bosons interacting in a two-dimensional harmonic trap

2020

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A system of bosons in a two-dimensional harmonic trap with the presence of Rashba-type spinorbit coupling is investigated. An analytic treatment of the ground state of a single atom in the weak-coupling regime is presented and used as a basis for a perturbation theory in the interacting two-boson system. The numerical diagonalization of both the single-particle and the two-boson Hamiltonian matrices allows us to go beyond those approximations and obtain not only the ground state, but also the low-energy spectra and the different energy contributions separately. We show that the expectation value of the spin-orbit term is related to the expectation value ofσzLz for the eigenstates of the system, regardless of the trapping potential. The ground state of the repulsively interacting two-boson system is characterized. With the presence of a sufficiently strong interaction and spin-orbit coupling strength, there is an energy-level crossing in the ground state of the system that changes its structure. This is reflected in a discontinuity in the different energy terms and it is signaled in the spatial density of the system.

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Statistical properties of spectra in harmonically trapped spin–orbit coupled systems

Cited by 16 publications

References 59 publications

Properties of spin–orbit-coupled Bose–Einstein condensates

Properties of spin–orbit-coupled Bose–Einstein condensates

Energy-level repulsion by spin-orbit coupling in two-dimensional Rydberg excitons

Spin-orbit-coupled bosons interacting in a two-dimensional harmonic trap

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