Solution of a Hamiltonian of quantum dots with Rashba spin–orbit coupling: quasi-exact solution

Tutunculer, Hayriye; Koc, Ramazan; Olğar, Eser

doi:10.1088/0305-4470/37/47/011

Cited by 19 publications

(22 citation statements)

References 34 publications

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“…This was in fact also done in Ref. [35]. However, for the condensate considered in this work, such a trapping potential is almost exclusively present in experiments, while this is not the case for the electrons in semiconducting quantum-dots of Ref.…”

Section: Model Systemsupporting

confidence: 65%

“…However, for the condensate considered in this work, such a trapping potential is almost exclusively present in experiments, while this is not the case for the electrons in semiconducting quantum-dots of Ref. [35]. By properly Stark shifting the internal atomic states, individual trapping potentials can be achieved.…”

Section: Model Systemmentioning

confidence: 93%

“…The spin-orbit coupling is on a Rashba-form [33], which has been frequently studied in the context of semiconductor quantum-dots [34,35].…”

Section: Model Systemmentioning

confidence: 99%

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Jahn-Teller-induced Berry phase in spin-orbit-coupled Bose-Einstein condensates

Larson

Sjöqvist

2009

Phys. Rev. A

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We demonstrate that Berry phases may greatly affect the dynamics of spin-orbit coupled BoseEinstein condensates. The effective model Hamiltonian under consideration is shown to be equivalent to the E × ε Jahn-Teller model first introduced in molecular physics. The corresponding conical intersection is identified and the Berry phase acquired for a wave packet encircling the intersection studied. It is found that this phase manifests itself in the density profile of the condensate, making it a directly measurable quantity via time-of-flight detection. Moreover, the non-Abelian gauge structure of the system is addressed and we verify how it affects the dynamics.

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Section: Model Systemsupporting

confidence: 65%

Section: Model Systemmentioning

confidence: 93%

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Jahn-Teller-induced Berry phase in spin-orbit-coupled Bose-Einstein condensates

Larson

Sjöqvist

2009

Phys. Rev. A

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“…(2) and (3), H (12) soc,a ( r 12 ) and H (12) soc,soc ( r 12 ) account for the atom-atom interaction. We note that the single particle Hamiltonian H (1) ( r j ) and variants thereof have been investigated extensively in quantum optics and molecular physics [40,41]. In quantum optics the Hamiltonian is referred to as the Jaynes-Cummings Hamiltonian.…”

Section: System Hamiltonianmentioning

confidence: 99%

Harmonically trapped two-atom systems: Interplay of short-ranges-wave interaction and spin-orbit coupling

Yin

Gopalakrishnan²,

Blume

2014

Phys. Rev. A

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The coupling between the spin degrees of freedom and the orbital angular momentum has a profound effect on the properties of nuclei, atoms and condensed matter systems. Recently, synthetic gauge fields have been realized experimentally in neutral cold atom systems, giving rise to a spin-orbit coupling term with "strength" kso. This paper investigates the interplay between the single-particle spin-orbit coupling term of Rashba type and the short-range two-body s-wave interaction for cold atoms under external confinement. Specifically, we consider two different harmonically trapped two-atom systems. The first system consists of an atom with spin-orbit coupling that interacts with a structureless particle through a short-range two-body potential. The second system consists of two atoms that both feel the spin-orbit coupling term and that interact through a short-range two-body potential. Treating the spin-orbit term perturbatively, we determine the correction to the ground state energy for various generic parameter combinations. Selected excited states are also treated. An important aspect of our study is that the perturbative treatment is not limited to small s-wave scattering lengths but provides insights into the system behavior over a wide range of scattering lengths, including the strongly-interacting unitary regime. We find that the interplay between the spin-orbit coupling term and the s-wave interaction generically enters, depending on the exact parameter combinations of the s-wave scattering lengths, at order k 2 so or k 4 so for the ground state and leads to a shift of the energy of either sign. While the absence of a term proportional to kso follows straightforwardly from the functional form of the spin-orbit coupling term, the absence of a term proportional to k 2 so for certain parameter combinations is unexpected. The well-known fact that the spin-orbit coupling term couples the relative and center of mass degrees of freedom has interesting consequences for the trapped two-particle systems. For example, we find that the spin-orbit coupling term turns, for certain parameter combinations, sharp crossings into avoided crossings with an energy splitting proportional to kso. Our perturbative results are confirmed by numerical calculations that expand the eigenfunctions of the two-particle Hamiltonian in terms of basis functions that contain explicitly correlated Gaussians.

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“…On the other hand, a spin transistor can also be achieved by using only nonmagnetic materials that exploit the unique characteristics of bulk inversion asymmetry in (110)-oriented semiconductor heterostructures, as reported by Hall et al [6][7]. Furthermore, Voskoboynikov et al have proposed that a non-magnetic semiconductor material can be produced by Rashba spin-orbit coupling due to the Dresselhaus effect occurring in zinc-blende [8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Transmittance and Tunneling Current through a Trapezoidal Barrier under Spin Polarization Consideration

Noor

Nabila

Mardianti

et al. 2018

J. Phys.: Conf. Ser.

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Abstract.The transmittance and tunneling current in heterostructures under spin polarization consideration were studied by employing a zinc-blended structure for the heterostructures. An electron tunnels through a potential barrier by applying a bias voltage to the barrier, which is called the trapezoidal potential barrier. In order to study the transmittance, an Airy wave function approach was employed to find the transmittance. The obtained transmittance was then utilized to compute the tunneling current by using a Gauss quadrature method. It was shown that the transmittances were asymmetric with the incident angle of the electron. It was also shown that the tunneling currents increased as the bias voltage increased.

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Solution of a Hamiltonian of quantum dots with Rashba spin–orbit coupling: quasi-exact solution

Cited by 19 publications

References 34 publications

Jahn-Teller-induced Berry phase in spin-orbit-coupled Bose-Einstein condensates

Jahn-Teller-induced Berry phase in spin-orbit-coupled Bose-Einstein condensates

Harmonically trapped two-atom systems: Interplay of short-ranges-wave interaction and spin-orbit coupling

Transmittance and Tunneling Current through a Trapezoidal Barrier under Spin Polarization Consideration

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