Spectroscopic probes of isolated nonequilibrium quantum matter: Quantum quenches, Floquet states, and distribution functions

Abstract

We investigate radio-frequency (rf) spectroscopy, metal-to-superconductor tunneling, and angle-resolved photoemission spectroscopy (ARPES) as probes of isolated out-of-equilibrium quantum systems, and examine the crucial role played by the nonequilibrium distribution function. As an example, we focus on the induced topological time-periodic (Floquet) phase in a two-dimensional p + ip superfluid, following an instantaneous quench of the coupling strength. The post-quench Cooper pairs occupy a linear combination of "ground" and "excited" Floquet states, with coefficients determined by the distribution function. While the Floquet band structure exhibits a single avoided crossing relative to the equilibrium case, the distribution function shows a population inversion of the Floquet bands at low energies. For a realization in ultracold atoms, these two features compensate, producing a bulk average rf signal that is well captured by a quasiequilibrium approximation. In particular, the rf spectrum shows a robust gap. The single crossing occurs because the quench-induced Floquet phase belongs to a particular class of soliton dynamics for the BCS equation. The population inversion is a consequence of this, and ensures the conservation of the pseudospin winding number. As a comparison, we compute the rf signal when only the lower Floquet band is occupied; in this case, the gap disappears for strong quenches. The tunneling signal in a solid-state realization is ignorant of the distribution function, and can show wildly different behaviors. We also examine rf, tunneling, and ARPES for weak quenches, such that the resulting topological steady state is characterized by a constant nonequilibrium order parameter. In a system with a boundary, tunneling reveals the Majorana edge states. However, the local rf signal due to the edge states is suppressed by a factor of the inverse system size, and is spatially deconfined throughout the bulk of the sample.

Twisting Anderson pseudospins with light: Quench dynamics in terahertz-pumped BCS superconductors

“…Large quenches from weak to strong pairing (∆ i ≪ ∆ f ) can induce phase III, in which ∆(t) exhibits persistent oscillations [17,22]. Phase III is a selfgenerated Floquet phase without external periodic driving [42,43], and is connected to the instability of the normal state.…”

“…Due mainly to the integrability of the BCS model [18,19,21], many asymptotically exact results are already known. The most important is the identification of three different nonequilibrium phases (dubbed "I, II, and III" in [28,41], reviewed below), predicted to occur in quenches of an s-wave superconductor [22,23], p+ip superfluid [41][42][43], BCS-BEC condensate [24,28,36], and spin-orbit-coupled fermion condensate [44,45].…”

Integrable Floquet dynamics

“…Using this criterion any Floquet system, which can be mapped to a static system via a local rotation (e.g. a static system in the rotating frame) is integrable because its folded spectrum contains infinitely many level crossings [17,18]. The Floquet integrable systems defined in this way do not heat up even at infinite times exhibiting localization in energy space [19][20][21][22][23][24][25][26], which in many respects very similar to the localization in real space in disordered models.…”

Topology and entanglement in quench dynamics

“…In a two-band Chern insulator, the dynamics of the post-quench state can be captured by the Hopf number 14,15 . The post-quench dynamics across a quantum critical point is also influenced by the topological edge states [16][17][18][19][20] . The topology of the static Hamiltonian and topology of the post-quench state are related.…”