Nonequilibrium Landau-Zener tunneling in exciton-polariton condensates

Abstract

For describing a coherent quantum two-level system driven by a linearly time-dependent detuning, the Landau-Zener model is routine to serve as a textbook model of its dynamics. Along this research line, a particularly intriguing question is whether such framework can be extended to capture an intrinsic nonequilibrium nature for a quantum system with coherent and dissipative dynamics occurring on an equal footing. In this work, we are motivated to investigate the Landau-Zener problem of polariton condensates in a periodic potential under nonresonant pumping by using the driven-dissipative Gross-Pitaevskii equations coupled to the rate equation. Within the two-mode approximation, a nonequilibrium Landau-Zener model, characterized by coherent and dissipative dynamics occurring on an equal footing, are derived. Fundamentally different from the previous Landau-Zener model, the total density of nonequilibrium Landau-Zener model general is not the conserved quantity anymore due to the dissipative nature. In surprise, the parameter regimes of the total density still being conserved can still be found. The motion of Hamiltonian of non-equilibrium Landau-Zener problem in phase space is further discussed, which is directly corresponding to the tunneling rate. The instability of the band structure can also be studied by the curvatures in phase space and there may be two loops in the middle of the Brillouin zone. Detailed analysis on the non-equlibrium nature on the tunneling rate will open a new perspective toward understanding the Landau-Zener problem.

Topological Landau–Zener nanophotonic circuits

“…The Landau–Zener (LZ) model, initially established to study the dynamics in a two-level quantum system, 28 , 29 can be employed to predict the probability of nonadiabatic tunneling between two energy levels 30 , 31 . This model has been widely applied to investigate the tunneling effect in condensed matter physics, 32 , 33 multi-particle systems, 34 , 35 optical structures, 36 – 38 and acoustics 39 . The LZ model provides an easy yet effective way to modulate/control the light transport due to its flexible and convenient realization in 2D optical circuits.…”

Quantum nonequilibrium dynamics from Knizhnik-Zamolodchikov equations

“…There has been considerable interest in nonequilibrium dynamics of quantum systems (see e.g., refs. [1,2]) over the last couple of decades that surged again recently in connection with quantum information problems [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. These include the dynamical discrete-state Bardeen-Cooper-Shriffer (BCS) pairing models [5,[20][21][22][23][24][25][26][27][28][29][30][31][32][33], where for example the interaction strength can be made time dependent, and various multi-level Landau-Zenner tunneling models and their many body generalizations [34][35][36][37][38][39][40][41][42][43][44][45][46].…”

Interaction-induced double-sided skin effect in an exciton-polariton system

“…Moreover, due to the photons escaping from the microcavity, exciton-polaritons are noticeably an open quantum (non-Hermitian) system, which requires additional pumping to maintain a steady state in the system [5]. This character makes the exciton-polariton system an ideal platform to study non-Hermitian transitions with gain and loss [6,7]. Although various research has been done in the Hermitian regime to realize polariton topological phases, with the interplay between Zeeman shift resulting from the application of magnetic field and the transverse electric-transverse magnetic (TE-TM) splitting of the photonic modes [8][9][10][11][12], accounting for nonlinearity [13,14], and using the polarization splitting of elliptical micropillars [15], several works have been reported in recent years to explore the non-Hermitian physics in the exciton-polariton system.…”