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(Color online) Schematic of the DP mechanism of the spin relaxation under the weak (a) and strong (b) effective Zeeman magnetic fields. Due to the random momentum scattering, the k-dependent magnetic field changes from (k 1 ) to (k 3 ) and the spin vector S(k) precesses around the k-dependent magnetic field during the free flight between adjacent scattering events. With the weak effective Zeeman magnetic field, this causes the conventional DP spin relaxation. With the strong effective Zeeman magnetic field satisfying |(k)||, tot (k) is nearly parallel to the effective Zeeman magnetic field = ˆ z and the DP spin relaxation shows anomalous behaviors.
Source publication
We report the anomalous D'yakonov-Perel' spin relaxation in ultracold
spin-orbit-coupled 40K gas when the coupling between
|9/2,9/2> and |9/2,7/2> states, acting as an effective Zeeman
magnetic field, is much stronger than the spin-orbit coupled field. Both
the transverse and longitudinal spin relaxations are investigated with
small and large spin...
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Citations
... Spin dynamics for Fermi gas with spinorbital coupling has been discussed in Refs. [30][31][32][33][34][35][36][37]. ...
In this Letter, we investigate spin dynamics of a two-component Bose gas with spin-orbit coupling realised in cold atom experiments. We derive coupled hydrodynamic equations for number and spin densities as well as their associated currents. Specialising to quasi-one-dimensional situation, we obtain analytic solutions of the spin helix structure and its dynamics in both adiabatic and diabatic regimes. In the adiabatic regime, the transverse spin decays parabolically in the short-time limit and exponentially in the long time limit, depending on initial polarisation. In contrast, in the diabatic regime, transverse spin density and current oscillate in a way similar to the charge-current oscillation in an undamped LC circuit. The effects of Rabi coupling on the short-time spin dynamics is also discussed. Finally, using realistic experimental parameters for $^{87}$Rb, we show that the time scales for spin dynamics is of order of milliseconds to a few seconds and can be observed experimentally.
... In recent years, the experimental breakthrough, realizing a synthetic SOC for (pseudo) spin-1/2 bosonic [2] and fermions [3,4], has provided a platform for quantum simulation of exotic states in condensed matter physics and a flexible tool for manipulating cold atoms, see review [5,6]. In particular, the static and dynamical properties, relevant to the SOC effects, have been extensively investigated in such atomic systems [8][9][10][11][12][13][14][15][16], which open new possibility to probe or control quantum spin dynamics such as spin relaxation, Zitterbewegung, spin resonance, and the spin-Hall effect. ...
We investigate fast transport and spin manipulation of tunable spin-orbit-coupled Bose-Einstein condensates in a moving harmonic trap. Motivated by the concept of "shortcuts to adiabaticity", we design inversely the time-dependent trap position and spin-orbit coupling strength. By choosing appropriate boundary conditions we obtain fast transport and spin flip simultaneously. The non-adiabatic transport and relevant spin dynamics are illustrated with numerical examples, and compared with the adiabatic transport with constant spin-orbit-coupling strength and velocity. Moreover, the influence of nonlinearity induced by interatomic interaction is discussed in terms of the Gross-Pitaevskii approach, showing the robustness of the proposed protocols. With the state-of-the-art experiments, such inverse engineering technique paves the way for coherent control of spin-orbit-coupled Bose-Einstein condensates in harmonic traps.
... For the Bose system, the spin dynamics of the Bose-Einstein condensation has attracted much attention. [1][2][3][4][5][6][7][8] For the Fermi cold atoms, the systems without 9-25 and with [26][27][28][29][30][31][32] spin-orbit coupling (SOC) are extensively investigated. In the absence of the SOC, many interesting phenomena, such as the Leggett-Rice effect in unitary gas [17][18][19][20][21] and anomalous spin segregation in extremely weak scattering limit, [22][23][24][25] have enriched the understanding of the spin dynamics of Fermions. ...
... With the synthetic SOC experimentally realized by laser control technique in cold atoms, 7,8,26,27 the spin relaxation for the Fermi cold atoms with SOC has been studied both experimentally [26][27][28] and theoretically. [29][30][31][32] This is partly motivated by the wellcontrolled laser technique, which provides more freedom for the cold atoms than the conventional solids. On one hand, rich regimes can be realized by tuning the SOC strength; on the other hand, not only the interatom interaction can be tuned by the Feshbach resonance, 33 but also the atom-disorder interaction can be introduced and controlled by the speckle laser technique. ...
... In above equation, k = (k x , k y , k z ) denotes the centerof-mass momentum of the atom; Ω acts as an effective Zeeman field along thex-direction; δ is the Raman detuning, which is set to be zero in our work; Ω z (k) = αk x represents the k-dependent effective magnetic field along theẑ-direction, which is perpendicular to the Zeeman field, with |α| being the strength of the spin-orbit coupled field. With this specific effective magnetic field Ω(k) by setting δ = 0, it has been revealed that both the conventional 29,30,32 and anomalous 31,38,39 D'yakonov-Perel' (DP) 40 spin relaxations can be realized with |Ω z (k)| Ω and |Ω z (k)| ≪ Ω, respectively. For the conventional situation, in the strong (weak) scattering limit when |Ω(k)| τ * k ≪ 1 ( |Ω(k)| τ * k 1), the spin relaxation time (SRT) τ s is inversely proportional (proportional) to the momentum scattering time τ * k . ...
We investigate the steady-state spin diffusion for ultracold spin-orbit
coupled $^{40}$K gas by the kinetic spin Bloch equation approach both
analytically and numerically. Four configurations, i.e., the spin diffusions
along two specific directions with the spin polarization perpendicular
(transverse configuration) and parallel (longitudinal configuration) to the
effective Zeeman field are studied. It is found that the behaviors of the
steady-state spin diffusion for the four configurations are very different,
which are determined by three characteristic lengths: the mean free path
$l_{\tau}$, the Zeeman oscillation length $l_{\Omega}$ and the spin-orbit
coupling oscillation length $l_{\alpha}$. It is analytically revealed and
numerically confirmed that by tuning the scattering strength, the system can be
divided into {\it five} regimes: I, weak scattering regime ($l_{\tau}\gtrsim
l_{\Omega}, l_{\alpha}$); II, Zeeman field-dominated moderate scattering regime
($l_{\Omega}\ll l_{\tau}\ll l_{\alpha}$); III, spin-orbit coupling-dominated
moderate scattering regime ($l_{\alpha}\ll l_{\tau}\ll l_{\Omega}$); IV,
relatively strong scattering regime ($l_{\tau}^c\ll l_{\tau}\ll l_{\Omega},
l_{\alpha}$); V, strong scattering regime ($l_{\tau}\ll l_{\Omega},
l_{\alpha},l_{\tau}^c$), with $l_{\tau}^c$ representing the crossover length
between the relatively strong and strong scattering regimes. In different
regimes, the behaviors of the spacial evolution of the steady-state spin
polarization are very rich, showing different dependencies on the scattering
strength, Zeeman field and spin-orbit coupling strength. The rich behaviors of
the spin diffusions in different regimes are hard to be understood in the
framework of the simple drift-diffusion model or the direct inhomogeneous
broadening picture in the literature. ...
... Starting with a fully polarized Fermi sea, fermion with different momentum undergoes spin procession in different way, and soon the total spin oscillation will be damped, as observed in Ref. 2 . Recently, a number of theoretical papers have also studied spin diffusion in SO coupled Fermi gases [70][71][72][73] , whose predications can be verified in future experiments. ...
This review focuses on recent developments on studying synthetic spin-orbit
(SO) coupling in ultracold atomic gases. Two types of SO coupling are
discussed. One is Raman process induced coupling between spin and motion along
one of the spatial directions, and the other is Rashba SO coupling. We
emphasize their common features in both single-particle and two-body physics
and their consequences in many-body physics. For instance, single particle
ground state degeneracy leads to novel features of superfluidity and richer
phase diagram; increased low-energy density-of-state enhances interaction
effects; the absence of Galilean invariance and spin-momentum locking give rise
to intriguing behaviors of superfluid critical velocity and novel quantum
dynamics; and mixing of two-body singlet and triplet states yields novel
fermion pairing structure and topological superfluids. With these examples, we
show that investigating SO coupling in cold atom systems can enrich our
understanding of basic phenomena such as superfluidity, provide a good platform
for simulating condensed matter states such as topological superfluids, and
more importantly, result in novel quantum systems such as SO coupled unitary
Fermi gas or high spin quantum gases. Finally we also point out major
challenges and possible future directions.
... [10][11][12]), topological states (e.g. [13]), and nontrivial spin dynamics [14][15][16]. Flexibility in designing the fields suggests new applications of cold atoms in dynamical systems, for example, developing of new quantum measurement techniques. Below we use this coupling in order to simulate a measurement on spin precessing in an external magnetic field, a fundamental problem in many branches of physics. ...
We show that by switching on a spin-orbit interaction in a cold-atom system,
experiencing a Zeeman-like coupling to an external field, e.g., in a
Bose-Einstein condensate, one can simulate a quantum measurement on a
precessing spin. Depending on the realization, the measurement can access both
the ergodic and the Zeno regimes, while {the time dependence} of the spin's
decoherence may vary from a Gaussian to an inverse fractional power law. Back
action of the measurement forms time- and coordinate-dependent profiles of the
atoms' density, resulting in its translation, spin-dependent fragmentation, and
appearance of interference patterns.
... Experiments on spin-orbit coupled Fermi gases are already beginning to explore spin dynamics driven by SOC [8]. A systematic investigation of how spin dynamics is influenced by temperature and interactions is an active area of study [35,36], and is of considerable relevance to future experiments on strongly correlated spin-orbit coupled quantum gases. ...
We consider the time evolution of the magnetization in a Rashba spin-orbit coupled Fermi gas, starting from a fully polarized initial state. We model the dynamics using a Boltzmann equation, which we solve in the Hartree-Fock approximation. The resulting nonlinear system of equations gives rise to three distinct dynamical regimes with qualitatively different asymptotic behaviors of the magnetization at long times. The distinct regimes and the transitions between them are controlled by the ratio of interaction and spin-orbit coupling strength λ: for small λ, the magnetization decays to zero. For intermediate λ, it displays undamped oscillations about zero, and for large λ, a partially magnetized state is dynamically stabilized. The dynamics we find is a spin analog of interaction induced self-trapping in double-well Bose Einstein condensates. The predicted phenomena can be realized in trapped Fermi gases with synthetic spin-orbit interactions.
... These results are consistent with our recent work in the three-dimensional spin-orbit-coupled ultracold Fermi gas, with similar effective magnetic fieldcreated by the Raman beams. 33,34 However, in the two dimensional electron gas (2DEG) system, new features arise due to the k-dependent Coulomb potential, which is different from the contact potential, i.e., constant V in the cold atom system. 33,[35][36][37][38] With the Coulomb potential, the HF effective magnetic field [Eq. ...
... 33,34 However, in the two dimensional electron gas (2DEG) system, new features arise due to the k-dependent Coulomb potential, which is different from the contact potential, i.e., constant V in the cold atom system. 33,[35][36][37][38] With the Coulomb potential, the HF effective magnetic field [Eq. (2)] is also k-dependent and not exactly along the direction of the spin polarization (In the cold atom system, Ω HF is always antiparallel to the spin polarization 33 ). ...
... With weak HF effective magnetic field [ |Ω HF (k)| ≪ |Ω|], for the transverse (longitudinal) spin relaxation, the HF effective magnetic field acts as a rotating (static) magnetic field around (along) the Zeeman field. 33 In this situation, for the electronimpurity scattering, which is elastic, the transverse (longitudinal) SRT is expressed in Eq. We first analyze the transverse spin relaxation [ Fig. 1(a)]. ...
We investigate the influence of the Hartree-Fock self-energy, acting as an
effective magnetic field, on the anomalous D'yakonov-Perel' spin relaxation in
InAs (110) quantum wells when the magnetic field in the Voigt configuration is
much stronger than the spin-orbit-coupled field. The transverse and
longitudinal spin relaxations are discussed both analytically and numerically.
For the transverse configuration, it is found that the spin relaxation is very
sensitive to the Hartree-Fock effective magnetic field, which is very different
from the conventional D'yakonov-Perel' spin relaxation. Even an extremely small
spin polarization ($P=0.1\%$) can significantly influence the behavior of the
spin relaxation. It is further revealed that this comes from the {\em unique}
form of the effective inhomogeneous broadening, originated from the mutually
perpendicular spin-orbit-coupled field and strong magnetic field. It is shown
that this effective inhomogeneous broadening is very small and hence very
sensitive to the Hartree-Fock field. Moreover, we further find that in the spin
polarization dependence, the transverse spin relaxation time decreases with the
increase of the spin polarization in the intermediate spin polarization regime,
which is also very different from the conventional situation, where the spin
relaxation is always suppressed by the Hartree-Fock field. It is revealed that
this {\em opposite} trends come from the additional spin relaxation channel
induced by the HF field. For the longitudinal configuration, we find that the
spin relaxation can be either suppressed or enhanced by the Hartree-Fock field
if the spin polarization is parallel or antiparallel to the magnetic field.
In this Letter, we investigate spin dynamics of a two-component Bose gas with spin-orbit coupling realized in cold atom experiments. We derive coupled hydrodynamic equations for number and spin densities as well as their associated currents. Specializing to the quasi-one-dimensional situation, we obtain analytic solutions of the spin helix structure and its dynamics in both adiabatic and diabatic regimes. In the adiabatic regime, the transverse spin decays parabolically in the short-time limit and exponentially in the long-time limit, depending on initial polarization. In contrast, in the diabatic regime, transverse spin density and current oscillate in a way similar to the charge-current oscillation in an undamped LC circuit. The effects of Rabi coupling on the short-time spin dynamics is also discussed. Finally, using realistic experimental parameters for Rb87, we show that the timescales for spin dynamics is of the order of milliseconds to a few seconds and can be observed experimentally.
Achieving full control of a Bose-Einstein condensate can have valuable applications in metrology, quantum information processing, and quantum condensed matter physics. We propose protocols to simultaneously control the internal (related to its pseudospin-1/2) and motional (position-related) states of a spin-orbit-coupled Bose-Einstein condensate confined in a Morse potential. In the presence of synthetic spin-orbit coupling, the state transition of a noninteracting condensate can be implemented by Raman coupling and detuning terms designed by invariant-based inverse engineering. The state transfer may also be driven by tuning the direction of the spin-orbit-coupling field and modulating the magnitude of the effective synthetic magnetic field. The results can be generalized for interacting condensates by changing the time-dependent detuning to compensate for the interaction. We find that a two-level algorithm for the inverse engineering remains numerically accurate even if the entire set of possible states is considered. The proposed approach is robust against the laser-field noise and systematic device-dependent errors.
We show that dynamics in spin-orbit coupling field simulates the von Neumann
measurement of a particle spin. We demonstrate how the measurement influences
the spin and coordinate evolution of a particle by comparing two examples of
such a procedure. First example is a simultaneous measurement of spin
components, $\sigma _{x}$ and $\sigma _{y}$, corresponding to non-commuting
operators, which cannot be accurately obtained together at a given time instant
due to the Heisenberg uncertainty ratio. By mapping spin dynamics onto a
spatial walk such a procedure determines measurement-time averages of $\sigma
_{x}$ and $\sigma _{y}$, which already can be precisely evaluated in a single
short-time measurement. The other, qualitatively different, example is the spin
of a one-dimensional particle in a magnetic field. Here the outcome depends on
the angle between the spin-orbit coupling and magnetic fields. These results
can be applied to studies of spin-orbit coupled cold atoms and electrons in
solids.
