Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2406.01619 · Physical Review A

Magnetically generated spin-orbit coupling for ultracold atoms with slowly varying periodic driving

D. Burba, Mažena Mackoit-Sinkevičienė, Viktor Novičenko, Emilia Witkowska, Gediminas Juzeliūnas

Published May 30, 2024• 0 citations
arXivHTMLPDF

Abstract

The spin-orbit coupling (SOC) affecting the center of mass of ultracold atoms can be simulated using a properly chosen periodic sequence of magnetic pulses. Yet such a method is generally accompanied by micromotion, which hinders precise control of atomic dynamics, thus complicating practical applications. Here we show how to bypass the micromotion emerging in the magnetically induced SOC by properly switching on and off the oscillating magnetic fields at the initial and final times. We consider the exact dynamics of the system and demonstrate that the overall dynamics can be immune to the micromotion. The exact dynamics is shown to agree well with the evolution of the system described by the slowly changing effective Floquet Hamiltonian including the SOC term. The agreement is shown to be best when the phase of the periodic driving takes a specific value for which the effect of the spin-orbit coupling is maximum.

DOI
10.1103/physreva.109.053319

Related papers

Tunable atomic spin-orbit coupling synthesized with a modulating gradient magnetic field

Xinyu Luo, Ling-Na Wu, Ji-Yao Chen +5 more

We report the observation of synthesized spin-orbit coupling (SOC) for ultracold spin-1 (87)Rb atoms. Different from earlier experiments where a one dimensional (1D) atomic SOC of pseudo-spin-1/2 is synthesized with Raman laser fields, the scheme we demonstrate employs a gradient magnetic field (GMF) and ground-state atoms, thus is immune to atomic spontaneous emission. The strength of SOC we realize can be tuned by changing the modulation amplitude of the GMF, and the effect of the SOC is confirmed through the studies of: 1) the collective dipole oscillation of an atomic condensate in a harmonic trap after the synthesized SOC is abruptly turned on; and 2) the minimum energy state at a finite adiabatically adjusted momentum when SOC strength is slowly ramped up. The condensate coherence is found to remain very good after driven by modulating GMFs. Our scheme presents an alternative means for studying interacting many-body systems with synthesized SOC.

arXiv:1502.07091•Scientific Reports•Jan 11, 2016•118 citations

Non-Abelian geometric potentials and spin-orbit coupling for periodically driven systems

Povilas Račkauskas, Viktor Novičenko, Han Pu +1 more

We demonstrate the emergence of the non-Abelian geometric potentials and thus the three-dimensional (3D) spin-orbit coupling (SOC) for ultracold atoms without using the laser beams. This is achieved by subjecting an atom to a periodic perturbation which is the product of a position-dependent Hermitian operator $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{V}\left(\mathbf{r}\right)$ and a fast oscillating periodic function $f\left(\ensuremath{\omega}t\right)$ with a zero average. To have a significant spin-orbit coupling, we analyze a situation where the characteristic energy of the periodic driving is not necessarily small compared to the driving energy $\ensuremath{\hbar}\ensuremath{\omega}$. Applying a unitary transformation to eliminate the original periodic perturbation, we arrive at a non-Abelian (noncommuting) vector potential term describing the 3D SOC. The general formalism is illustrated by analyzing the motion of an atom in a spatially inhomogeneous magnetic field oscillating in time. A cylindrically symmetric magnetic field provides the SOC involving the coupling between the spin $\mathbf{F}$ and all three components of the orbital angular momentum (OAM) $\mathbf{L}$. In particular, the spherically symmetric monopole-type synthetic magnetic field $\mathbf{B}\ensuremath{\propto}\mathbf{r}$ generates the 3D SOC of the $\mathbf{L}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{F}$ form, which resembles the fine-structure interaction of hydrogen atom. However, the strength of the SOC here goes as $1/{r}^{2}$ for larger distances, instead of $1/{r}^{3}$ as in atomic fine structure. Such a longer-ranged SOC significantly affects not only the lower states of the trapped atom, but also the higher ones. Furthermore, by properly tailoring the external trapping potential, the ground state of the system can occur at finite OAM, while the ground state of hydrogen atom has zero OAM.

arXiv:1908.11275•Physical Review A•Dec 6, 2019•2 citations

Periodic driving control of Raman-induced spin-orbit coupling in Bose-Einstein condensates: The heating mechanisms

Jose M. Gomez Llorente, Jesús Plata

We focus on a technique recently implemented for controlling the magnitude of synthetic spin-orbit coupling (SOC) in ultracold atoms in the Raman-coupling scenario. This technique uses a periodic modulation of the Raman-coupling amplitude to tune the SOC. Specifically, it has been shown that the effect of a high-frequency sinusoidal modulation of the Raman-laser intensity can be incorporated into the undriven Hamiltonian via effective parameters, whose adiabatic variation can therefore be used to tune the SOC. Here, we characterize the heating mechanisms that can be relevant to this method. We identify the main mechanism responsible for the heating observed in the experiments as basically rooted in driving-induced transfer of population to excited states. Characteristics of that process determined by the harmonic trapping, the decay of the excited states, and the technique used for preparing the system are discussed. Additional heating, rooted in departures from adiabaticity in the variation of the effective parameters, is also described. Our analytical study provides some clues that may be useful in the design of strategies for curbing the effects of heating on the efficiency of the control methods.

arXiv:1606.08800•Physical Review A•Jun 28, 2016•8 citations

Atomic spin-orbit coupling synthesized with magnetic-field-gradient pulses

Zhi-Fang Xu, Li You, Masahito Ueda

We discuss a general scheme for creating atomic spin-orbit coupling (SOC) such as the Rashba or Dresselhaus types using magnetic-field-gradient pulses. In contrast to conventional schemes based on adiabatic center-of-mass motion with atomic internal states restricted to a dressed-state subspace, our scheme works for the complete subspace of a hyperfine-spin manifold by utilizing the coupling between the atomic magnetic moment and external magnetic fields. A space-dependent pulsed magnetic field acts as an internal-state-dependent impulse, thereby coupling the atomic internal spin with its orbital center-of-mass motion, as in the Einstein--de Haas effect. This effective coupling can be dynamically manipulated to synthesize SOC of any type (Rashba, Dresselhaus, or any linear combination thereof). Our scheme can be realized with most experimental setups of ultracold atoms and is especially suited for atoms with zero nuclear spins.

arXiv:1306.2829•Physical Review A•Jun 25, 2013•113 citations

Atomic spin orbit coupling synthesized with gradient magnetic fields

Xinyu Luo, Ling-Na Wu, Ruquan Wang +1 more

Spin orbit coupling (SOC) for neutral atoms can be synthesized with pulsed or time modulating gradient magnetic field (GMF). This is confirmed through the studies of collective dipole oscillations for a spin-1 atomic condensate in a harmonic trap after abruptly turning on SOC and adiabatically adjusted equilibrium states when SOC strength is slowly ramped up. Further measurements reveal that SOC can be enhanced when the GMF modulation frequency approaches harmonic trap frequency. Additionally, we discuss how the technique of pulsed GMF can be used to synthesize space-period magnetic fields, or magnetic lattices.

Journal of Physics Conference Series•Sep 7, 2015•1 citation

Magnetically Generated Spin-Orbit Coupling for Ultracold Atoms

Brandon Anderson, Ian B. Spielman, Gediminas Juzeliūnas

We present a new technique for producing two- and three-dimensional Rashba-type spin-orbit couplings for ultracold atoms without involving light. The method relies on a sequence of pulsed inhomogeneous magnetic fields imprinting suitable phase gradients on the atoms. For sufficiently short pulse durations, the time-averaged Hamiltonian well approximates the Rashba Hamiltonian. Higher order corrections to the energy spectrum are calculated exactly for spin-1/2 and perturbatively for higher spins. The pulse sequence does not modify the form of rotationally symmetric atom-atom interactions. Finally, we present a straightforward implementation of this pulse sequence on an atom chip.

arXiv:1306.2606•Physical Review Letters•Sep 18, 2013•192 citations
The spin-orbit coupling (SOC) affecting the center of mass of ultracold atoms can be simulated using a properly chosen periodic sequence of magnetic pulses. Yet such a method is generally accompanied by micromotion, which hinders precise control of atomic dynamics, thus complicating practical applications. Here we show how to bypass the micromotion emerging in the magnetically induced SOC by properly switching on and off the oscillating magnetic fields at the initial and final times. We consider the exact dynamics of the system and demonstrate that the overall dynamics can be immune to the micromotion. The exact dynamics is shown to agree well with the evolution of the system described by the slowly changing effective Floquet Hamiltonian including the SOC term. The agreement is shown to be best when the phase of the periodic driving takes a specific value for which the effect of the spin-orbit coupling is maximum.
We report the observation of synthesized spin-orbit coupling (SOC) for ultracold spin-1 (87)Rb atoms. Different from earlier experiments where a one dimensional (1D) atomic SOC of pseudo-spin-1/2 is synthesized with Raman laser fields, the scheme we demonstrate employs a gradient magnetic field (GMF) and ground-state atoms, thus is immune to atomic spontaneous emission. The strength of SOC we realize can be tuned by changing the modulation amplitude of the GMF, and the effect of the SOC is confirmed through the studies of: 1) the collective dipole oscillation of an atomic condensate in a harmonic trap after the synthesized SOC is abruptly turned on; and 2) the minimum energy state at a finite adiabatically adjusted momentum when SOC strength is slowly ramped up. The condensate coherence is found to remain very good after driven by modulating GMFs. Our scheme presents an alternative means for studying interacting many-body systems with synthesized SOC.
We demonstrate the emergence of the non-Abelian geometric potentials and thus the three-dimensional (3D) spin-orbit coupling (SOC) for ultracold atoms without using the laser beams. This is achieved by subjecting an atom to a periodic perturbation which is the product of a position-dependent Hermitian operator $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{V}\left(\mathbf{r}\right)$ and a fast oscillating periodic function $f\left(\ensuremath{\omega}t\right)$ with a zero average. To have a significant spin-orbit coupling, we analyze a situation where the characteristic energy of the periodic driving is not necessarily small compared to the driving energy $\ensuremath{\hbar}\ensuremath{\omega}$. Applying a unitary transformation to eliminate the original periodic perturbation, we arrive at a non-Abelian (noncommuting) vector potential term describing the 3D SOC. The general formalism is illustrated by analyzing the motion of an atom in a spatially inhomogeneous magnetic field oscillating in time. A cylindrically symmetric magnetic field provides the SOC involving the coupling between the spin F\mathbf{F}F and all three components of the orbital angular momentum (OAM) L\mathbf{L}L. In particular, the spherically symmetric monopole-type synthetic magnetic field $\mathbf{B}\ensuremath{\propto}\mathbf{r}$ generates the 3D SOC of the $\mathbf{L}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{F}$ form, which resembles the fine-structure interaction of hydrogen atom. However, the strength of the SOC here goes as 1/r21/{r}^{2}1/r2 for larger distances, instead of 1/r31/{r}^{3}1/r3 as in atomic fine structure. Such a longer-ranged SOC significantly affects not only the lower states of the trapped atom, but also the higher ones. Furthermore, by properly tailoring the external trapping potential, the ground state of the system can occur at finite OAM, while the ground state of hydrogen atom has zero OAM.
We focus on a technique recently implemented for controlling the magnitude of synthetic spin-orbit coupling (SOC) in ultracold atoms in the Raman-coupling scenario. This technique uses a periodic modulation of the Raman-coupling amplitude to tune the SOC. Specifically, it has been shown that the effect of a high-frequency sinusoidal modulation of the Raman-laser intensity can be incorporated into the undriven Hamiltonian via effective parameters, whose adiabatic variation can therefore be used to tune the SOC. Here, we characterize the heating mechanisms that can be relevant to this method. We identify the main mechanism responsible for the heating observed in the experiments as basically rooted in driving-induced transfer of population to excited states. Characteristics of that process determined by the harmonic trapping, the decay of the excited states, and the technique used for preparing the system are discussed. Additional heating, rooted in departures from adiabaticity in the variation of the effective parameters, is also described. Our analytical study provides some clues that may be useful in the design of strategies for curbing the effects of heating on the efficiency of the control methods.
We discuss a general scheme for creating atomic spin-orbit coupling (SOC) such as the Rashba or Dresselhaus types using magnetic-field-gradient pulses. In contrast to conventional schemes based on adiabatic center-of-mass motion with atomic internal states restricted to a dressed-state subspace, our scheme works for the complete subspace of a hyperfine-spin manifold by utilizing the coupling between the atomic magnetic moment and external magnetic fields. A space-dependent pulsed magnetic field acts as an internal-state-dependent impulse, thereby coupling the atomic internal spin with its orbital center-of-mass motion, as in the Einstein--de Haas effect. This effective coupling can be dynamically manipulated to synthesize SOC of any type (Rashba, Dresselhaus, or any linear combination thereof). Our scheme can be realized with most experimental setups of ultracold atoms and is especially suited for atoms with zero nuclear spins.
Spin orbit coupling (SOC) for neutral atoms can be synthesized with pulsed or time modulating gradient magnetic field (GMF). This is confirmed through the studies of collective dipole oscillations for a spin-1 atomic condensate in a harmonic trap after abruptly turning on SOC and adiabatically adjusted equilibrium states when SOC strength is slowly ramped up. Further measurements reveal that SOC can be enhanced when the GMF modulation frequency approaches harmonic trap frequency. Additionally, we discuss how the technique of pulsed GMF can be used to synthesize space-period magnetic fields, or magnetic lattices.
We present a new technique for producing two- and three-dimensional Rashba-type spin-orbit couplings for ultracold atoms without involving light. The method relies on a sequence of pulsed inhomogeneous magnetic fields imprinting suitable phase gradients on the atoms. For sufficiently short pulse durations, the time-averaged Hamiltonian well approximates the Rashba Hamiltonian. Higher order corrections to the energy spectrum are calculated exactly for spin-1/2 and perturbatively for higher spins. The pulse sequence does not modify the form of rotationally symmetric atom-atom interactions. Finally, we present a straightforward implementation of this pulse sequence on an atom chip.