Optical lattice modulation spectroscopy for spin-orbit coupled bosons

Abstract

Interacting bosons with two "spin" states in a lattice show novel superfluid-insulator phase transitions in the presence of spin-orbit coupling. Depending on the parameter regime, bosons in the superfluid phase can condense to either a zero momentum state or to one or multiple states with finite momentum, leading to an unconventional superfluid phase. We study the response of such a system to modulation of the optical lattice potential. We show that the change in momentum distribution after lattice modulation shows distinct patterns in the Mott and the superfluid phase and these patterns can be used to detect these phases and the quantum phase transition between them. Further, the momentum resolved optical modulation spectroscopy can identify both the gapless (Goldstone) gapped amplitude (Higgs) mode of the superfluid phase and clearly distinguish between the superfluid phases with a zero momentum condensate and a twisted superfluid phase by looking at the location of these modes in the Brillouin zone. We discuss experiments which can test our theory.

Quantum correlations and entanglement in far-from-equilibrium spin systems

“…Second, while universality in equilibrium systems is explained by one of the most fundamental tools in physics, the renormalization group (RG), the required concepts and tools for generalizing it to far-fromequilibrium systems have yet to be developed (though some progress has been made in this direction, see for example Refs. [112][113][114][115][116][117][118][119][120][121][122][123]). …”

Tuning towards dynamic freezing using a two-rate protocol

“…The electric field E may be made timedependent by varying the Zeeman field used to generate it as a function of time 38 while the detailed method creating a time dependent J in realistic experimental situation has been discussed in Ref. 40. Following the convention used in previous studies on this model, we shall choose U/J(0) = 40, E 0 /J(0) = 10 and n 0 = 1 so that the dynamics takes the system through the critical point located E c = U + 1.83J…”

“…Another such class of phenomenon involves dynamic transition where the free energy density of a quantum system after a quench develops non-analyticities leading to sharp cusp-like features in it's Lochsmidt echo pattern at specific times [10][11][12][13][14] ; these transitions have no equilibrium analogs and can not be described by any local order parameter. Furthermore, the universality and the possibility of application of renormalization group (RG) methods to such driven systems has been a subject of recent research [15][16][17] ; such analysis also leads to a several interesting features involving RG flow and universality of driven systems which are qualitatively different from their equilibrium counterparts.…”

Stability of a Floquet Bose-Einstein condensate in a one-dimensional optical lattice

“…There also have been studies of non-dissipative interaction physics [37]. Our work has connections with broader studies of heating in periodically driven systems [38][39][40][41][42][43][44] .…”