Open Quantum System Simulation of Faraday's Induction Law via Dynamical Instabilities

Open Quantum System Simulation of Faraday’s Induction Law via Dynamical Instabilities

Elvia Colella, Arkadiusz Kosior, Farokh Mivehvar, and Helmut Ritsch

Phys. Rev. Lett. 128, 070603 – Published 17 February 2022

Abstract

We propose a novel type of a Bose-Hubbard ladder model based on an open quantum-gas–cavity-QED setup to study the physics of dynamical gauge potentials. Atomic tunneling along opposite directions in the two legs of the ladder is mediated by photon scattering from transverse pump lasers to two distinct cavity modes. The resulting interplay between cavity photon dissipation and the optomechanical atomic backaction then induces an average-density-dependent dynamical gauge field. The dissipation-stabilized steady-state atomic motion along the legs of the ladder leads either to a pure chiral current, screening the induced dynamical magnetic field as in the Meissner effect, or generates simultaneously chiral and particle currents. For a sufficiently strong pump the system enters into a dynamically unstable regime exhibiting limit-cycle and period-doubled oscillations. Intriguingly, an electromotive force is induced in this dynamical regime as expected from an interpretation based on Faraday’s law of induction for the time-dependent synthetic magnetic flux.

Received 9 March 2021
Revised 13 December 2021
Accepted 1 February 2022
Corrected 11 March 2022

DOI:https://doi.org/10.1103/PhysRevLett.128.070603

Physics Subject Headings (PhySH)

Cavity quantum electrodynamics Dissipative dynamics Spin-orbit coupling

Bose-Einstein condensates

Condensed Matter, Materials & Applied Physics

Corrections

11 March 2022

Correction: The omission of a support statement in the Acknowledgment section has been fixed.

Authors & Affiliations

Elvia Colella ^*, Arkadiusz Kosior, Farokh Mivehvar, and Helmut Ritsch

Institut für Theoretische Physik, Universität Innsbruck, A-6020 Innsbruck, Austria

^*elvia.colella@uibk.ac.at

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Vol. 128, Iss. 7 — 18 February 2022

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Images

Figure 1
Sketch of the setup. (a) A spinor BEC is loaded into a 1D tilted optical lattice perpendicular to the axis of a linear cavity. Neighboring sites are Raman coupled via two cavity modes with strengths $G_{a, b}$ and transversely applied laser fields with amplitudes $Ω_{a, b}$ . A microwave couples the two atomic states locally with strength $Ω$ . (b) Sketch of the atomic level structure and of the two independent two-photon Raman transitions inducing directional tunneling between neighboring lattice sites. (c) Effective mapping of the spinor BEC in the 1D lattice in panel (a) into a two-leg Bose-Hubbard ladder with cavity-assisted longitudinal hoppings and microwave-generated transverse tunneling.
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Figure 2
Single-particle phase diagram. (a) The steady-state phase diagram in the ${\sqrt{N} η / κ, Δ / κ}$ parameter plane. The self-consistent band structure exhibits three distinct phases: PB-M and PB-V, and PI-BL states. The color map indicates the photon imbalance $Δ n_{ph}$ . The red dashed curve separating the PB-M and the PB-V states has been obtained analytically [34]. The three phases intersect in a tricritical point indicated by the brown dot. Inset: The synthetic magnetic flux $Φ_{B} / Φ_{0 B}$ as a function of $Δ / κ$ . For $Δ / κ = - 0.5$ , (b) typical band structure $ε_{\pm} (q)$ in each phase corresponding to $\sqrt{N} η / κ = {0.08, 0.50, 1.00}$ . Other parameters are set to $L = 51$ , $U = Δ / 2 L$ , $Ω = 1$ , and $V = γ = 0$ .
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Figure 3
Many-body phase diagram. (a) Nonequilibrium phase diagram in the ${\sqrt{N} η / κ, \bar{n}}$ parameter plane. For $Δ / κ = - 6$ , the system exhibits only two of the steady-state phases of Fig. 2: the PB-M and the PI-BL states. The two phases are separated by the solid white line. The gray area indicates a region of dynamical instability with no steady state. The color map indicates the steady-state synthetic magnetic flux $Φ_{B}$ , clearly showing average-density dependence. The total photon number $n_{ph}$ (b) and the photon number difference $Δ n_{ph} / n_{ph}$ (c) are shown in the same parameter plane. Photon number saturates the scale in the bright blue region in (b). (d) Current patterns in the PB-M and the PI-BL states. Parameters are the same as Fig. 2, except $V N = 1$ , $γ = 0.1$ .
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Figure 4
Periodic nonlinear dynamics for high densities $\bar{n} = 1.42$ . The phase space trajectories of the two cavity-mode amplitudes $α$ (gray) and $β$ (black) for long-time dynamics with $\sqrt{N} η / κ = 1.3$ (a) and 1.55 (b) [outside of the phase diagram of Fig. 3]. Insets in panels (I): Time evolution of the magnetic flux (black) and e.m.f (dashed gray). Time evolution of the induced chiral $J_{c}$ (black), particle $J_{p}$ (dashed gray), and rung $J_{⊥}$ (dotted blue) currents (II), and of the total photon number $n_{ph}$ (black) and the photon number difference $Δ n_{ph}$ (dashed gray) (III). Panel (a) exhibits stable limit-cycle oscillations, while panel (b) shows period-doubled oscillations. Other parameters are the same as Fig. 3 for $N = 140$ .
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