Quantum Quenches in Free Field Theory: Universal Scaling at Any Rate

Quantum quenches display universal scaling in several regimes. For quenches which start from a gapped phase and cross a critical point, with a rate slow compared to the initial gap, many systems obey Kibble-Zurek scaling. More recently, a different scaling behaviour has been shown to occur when the quench rate is fast compared to all other physical scales, but still slow compared to the UV cutoff. We investigate the passage from fast to slow quenches in scalar and fermionic free field theories with time dependent masses for which the dynamics can be solved exactly for all quench rates. We find that renormalized one point functions smoothly cross over between the regimes.Comment: 40 pages; v2: a bit late, but it includes minor modifications to match published versio

Smooth and fast versus instantaneous quenches in quantum field theory

We examine in detail the relationship between smooth fast quantum quenches, characterized by a time scale $\delta t$, and {\em instantaneous quenches}, within the framework of exactly solvable mass quenches in free scalar field theory. Our earlier studies \cite{dgm1,dgm2} highlighted that the two protocols remain distinct in the limit $\delta t \rightarrow 0$ because of the relation of the quench rate to the UV cut-off, i.e., $1/\delta t\ll\Lambda$ always holds in the fast smooth quenches while $1/\delta t\sim\Lambda$ for instantaneous quenches. Here we study UV finite quantities like correlators at finite spatial distances and the excess energy produced above the final ground state energy. We show that at late times and large distances (compared to the quench time scale) the smooth quench correlator approaches that for the instantaneous quench. At early times, we find that for small spatial separation and small $\delta t$, the correlator scales universally with $\delta t$, exactly as in the scaling of renormalized one point functions found in earlier work. At larger separation, the dependence on $\delta t$ drops out. The excess energy density is finite (for finite $m\delta t$) and scales in a universal fashion for all $d$. However, the scaling behaviour produces a divergent result in the limit $m\delta t \rightarrow 0$ for $d\ge4$, just as in an instantaneous quench, where it is UV divergent for $d \geq 4$. We argue that similar results hold for arbitrary interacting theories: the excess energy density produced is expected to diverge for scaling dimensions $\Delta > d/2$.Comment: 52 pages; v2: minor modifications to match published versio

Electron spin interferometry using a semiconductor ring structure

A ring structure fabricated from GaAs is used to achieve interference of the net spin polarization of conduction band electrons. Optically polarized spins are split into two packets by passing through two arms of the ring in the diffusive transport regime. Optical pumping with circularly polarized light on one arm establishes dynamic nuclear polarization which acts as a local effective magnetic field on electron spins due to the hyperfine interaction. This local field causes one spin packet to precess faster than the other, thereby controlling the spin interference when the two packets are combined.Comment: 4 pages, 2 figure