Dynamical preparation of stripe states in spin-orbit-coupled gases

Letter

Dynamical preparation of stripe states in spin-orbit-coupled gases

J. Cabedo, J. Claramunt, and A. Celi

Phys. Rev. A 104, L031305 – Published 23 September 2021

Abstract

In spinor Bose-Einstein condensates, spin-changing collisions are a remarkable proxy to coherently realize macroscopic many-body quantum states. These processes have been, e.g., exploited to generate entanglement, to study dynamical quantum phase transitions, and proposed for realizing nematic phases in atomic condensates. In the same systems dressed by Raman beams, the coupling between spin and momentum induces a spin dependence in the scattering processes taking place in the gas. Here we show that, at weak couplings, such modulation of the collisions leads to an effective Hamiltonian which is equivalent to the one of an artificial spinor gas with spin-changing collisions that are tunable with the Raman intensity. By exploiting this dressed-basis description, we propose a robust protocol to coherently drive the spin-orbit-coupled condensate into the ferromagnetic stripe phase via crossing a quantum phase transition of the effective low-energy model in an excited state.

Received 2 February 2021
Revised 30 July 2021
Accepted 30 August 2021

DOI:https://doi.org/10.1103/PhysRevA.104.L031305

Physics Subject Headings (PhySH)

Cold atoms & matter waves Dynamical phase transitions Quantum phase transitions Spin-orbit coupling

Bose-Einstein condensates Spinor Bose-Einstein condensates

Atomic, Molecular & OpticalCondensed Matter, Materials & Applied Physics

Authors & Affiliations

J. Cabedo ¹, J. Claramunt ², and A. Celi ¹

¹Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain
²Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YW, United Kingdom

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Vol. 104, Iss. 3 — September 2021

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Images

Figure 1
Pseudospin dynamics in SOC BECs. (a) Dispersion bands of the dressed Hamiltonian ${\hat{H}}_{k}$ with $Ω = 0.65 E_{r}$ , $δ = 0$ , and $ε = Ω^{2} / 16 E_{r}$ . The color texture indicates the expected value of the spin of the dressed states. Dashed lines show the undressed dispersion bands. (b) Schematic representation of resonant collisions mediated by Raman transitions (represented by wavy lines) which act as effective spin-changing collisions. For weak Raman coupling and interactions, the dressed-state dynamics can be captured by the pseudospin Hamiltonian (4). (c i) Phase diagram of (4), as a function of the Raman Rabi frequency $Ω$ and effective quadratic Zeeman shift $ε$ , for ${}^{87}{Rb}$ at $n = 7.5 \times 10^{13} {cm}^{- 3}$ . The polar (P), twin-Fock (TF), and broken-axisymmetry (BA) phases meet at the tricritical point $C_{F}$ (black dot). (c ii) Corresponding phase diagram for the highest-excited eigenstate. The upper panel in the inset shows the energy gap between the two most excited eigenstates along the red dashed segment for $N = 1000$ . The lower panel shows the expected value of the collective pseudospin ${\hat{L}}^{2}$ (red dash-dotted line) and tensor magnetization ${\hat{L}}_{z z}$ (blue solid line).
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Figure 2
Crossing quantum phase transitions in an excited state. (a) Plot of $L_{z z}$ (blue solid line) and $L^{2}$ (red dashed line) as a function of $\tilde{ε}$ for a state initially prepared at $b_{\pm 1} = \sqrt{50}$ and $b_{0} = \sqrt{N - 100}$ , with $N (0) = 10^{4}$ and $ℏ ω_{t} = 2 π \times 140 Hz$ . The state is evolved under the GPE while driving $\tilde{ε}$ from $- 3 λ$ to $3 λ$ , keeping $Ω = 0.65 E_{r}$ , following the red dashed path in Fig. 1. The total drive time is set to $τ_{d} = 8 h / λ$ . The corresponding results obtained with simulations of the three-mode model (4) are shown in light colors. (b) Quasimomentum density $| \tilde{ψ} (p_{z}) |^{2}$ of the driven state at $\tilde{ε} = 0$ (dark green solid line) and $\tilde{ε} = 3 λ$ (light green dashed line). (c) Corresponding density profiles at $\tilde{ε} = 0$ (purple solid line) and $\tilde{ε} = 3 λ$ (pink dashed line).
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Figure 3
Robust preparation of FS states. (a) Plot of $L_{z z}$ (blue solid line), $L^{2}$ (red dashed line), and $f_{3 M}$ (green dash-dotted line) as a function of time for a state initially prepared at $b_{\pm 1} = \sqrt{10}$ and $b_{0} = \sqrt{N - 20}$ , with $N (0) = 10^{4}$ and $ℏ ω_{t} = 2 π \times 140 Hz$ . The state is evolved under the GPE while driving $\tilde{ε}$ from $- 3 λ$ to 0 by linearly increasing $Ω$ from $0.65 E_{r}$ to $0.767 E_{r}$ , following the blue dash-dotted path in Fig. 1. The parameters of the GPE are subject to random fluctuations that simulate experimental noise, as described in the text, and the values depicted are averaged over 20 realizations. The shadowed regions indicate the associated standard deviations. (b) Longitudinal density ${| ψ |}^{2}$ (blue solid line), spin density $F_{x}$ (red dashed line), and nematic density $N_{x x}$ (green dash-dotted line) at $t = 150$ ms from a single realization of the drive.
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