Floquet's Refrigerator: Conformal Cooling in Driven Quantum Critical Systems

Abstract

We propose a general method of cooling-periodic driving generated by spatially deformed Hamiltonians-and study it in general one-dimensional quantum critical systems described by a conformal field theory. Our protocol is able to efficiently cool a finite-temperature Gibbs (mixed) state down to zero temperature at prescribed sub-regions exponentially rapidly in Floquet time cycles. At the same time, entropy and energy are transferred and localized to the complementary regions that shrink with time. We derive these conclusions through an exact analytic solution of the full time evolution of reduced density matrices. We also use numerics in free-fermion lattice models as a benchmark and find remarkable agreement. Such conformal Floquet refrigerators open a promising new route to cooling synthetic quantum systems.

Quantum hypothesis testing in many-body systems

“…So if a point becomes infinitely hot, the rest of the circle must cool down. This gives a holographic picture for the Floquet refrigerator [97]. The emergence of a hot spot and its holographic interpretation with a deforming black hole horizon was observed in the context of time evolution after a SSD quench in [61].…”

“…This corresponds to an emergent hot spot in the CFT, a point that is heating while the rest of the system is cooling down [61]. This gives a holographic interpretation of the conformal Floquet refrigerator [97].…”

“…The relation between Virasoro process and spacetime metrics explains some of the observations in [63,96] related to the "emergent Rindler space". Effects related to dissipation and chaos were considered in [97][98][99]. Floquet CFTs are particularly interesting because they are relevant experimentally, see for example [100,101].…”

“…In the heating phase, the second term in (4.102) develops a sharpening peak (the position of which rotates around the circle), leading to a heating spot surrounded by a cooling region. This process was called as conformal Floquet cooling, and discussed in[97].…”

Thermodynamic geometry of ideal quantum gases: a general framework and a geometric picture of BEC-enhanced heat engines

“…A promising avenue towards scaling up the power and constancy of quantum thermal machines is to replace working systems with few degrees of freedom by many-body systems capable of hosting collective effects, which may lead to uncovering new mechanisms of energy conversion . Such effects, whose thermodynamics is yet to be fully understood, include: tunable interactions between particles, which can be used for work-extraction [44][45][46]; super-radiance and broken time-translation symmetry, which emerge in multi-level systems coupled to a thermal bath via collective observables [47][48][49][50][51][52]; quantum phase transitions [53][54][55][56] or quantum statistics, which provides a means of controlling an effective pressure that has no classical counterpart [57][58][59][60][61]. Thermodynamic geometry offers a powerful tool to analyse these phenomena from a unifying perspective and thus a potential avenue towards a universal framework describing how many-body effects can alter the performance of quantum thermal machines.…”