Preparation of Low Entropy Correlated Many-Body States via Conformal Cooling Quenches

We propose and analyze a method for preparing low entropy many-body states in isolated quantum optical systems of atoms, ions, and molecules. Our approach is based upon shifting entropy between different regions of a system by spatially modulating the magnitude of the effective Hamiltonian. We conduct two case studies, on a topological spin chain and the spinful fermionic Hubbard model, focusing on the key question: can a “conformal cooling quench” remove sufficient entropy within experimentally accessible timescales? Finite-temperature, time-dependent matrix product state calculations reveal that even moderately sized bath regions can remove enough energy and entropy density to expose coherent low-temperature physics. The protocol is particularly natural in systems with long-range interactions, such as lattice-trapped polar molecules and Rydberg-excited atoms, where the magnitude of the Hamiltonian scales directly with the interparticle spacing. To this end, we propose simple, near-term implementations of conformal cooling quenches in systems of atoms or molecules, where signatures of low-temperature phases may be observed.

Figure 1

(a) If the Hamiltonian in the bath region is related to the Hamiltonian in the “system” region by a constant rescaling, $H_B=\lambda H_S$, their entropy-energy-density curves satisfy $s_B(E)=s_S(E/\lambda )$. Thus preparing at state with constant entropy density establishes a temperature differential $T_B=\lambda T_S$, since $T=(dE/dS)$. (b) Schematic representation of particles or spins interacting through a long-range, power-law interaction $1/R^{\alpha }$. If the interparticle spacing on the left (bath) is increased by a factor $d$ relative to the right (system), then $H_B=(1/d{)}^{\alpha }{H}_S$. (c) In this case, a uniform Néel state has a temperature differential after reaching local equilibrium, and the resulting evolution will remove entropy from the right half of the chain as the system reaches global equilibrium.

Figure 2

Quench cooling of a 30-site spin-1 Haldane chain. After initializing the state at $t=0$ with uniform entropy density, the coupling constants ${\lambda }_x$ are scaled according to the bottom part of the figure, which should transport heat from the system on the right to the bath on the left. In the top part, we plot the change in energy density $h_x(t)-h_x(0)$ as the chain evolves.

Figure 3

The dynamical correlation function $C_{zz}(t)$ measured after four initialization protocols: (a) optimal, $C_{zz}(t)$ for the ground state of an $L=10$ chain; (b) finite $T=0.51J$, without a cooling quench. The edge coherence rapidly decays. (c) Finite $T_i=0.51J$, but starting the $C_{zz}$ measurement after the cooling quench shown in Fig. 2. The coherence is improved by an order of magnitude. (d) Same as (c), but eliminating the coupling between sites $i=20$ and 21 after the quench, which cuts off the bath.

Figure 4

Cooling dynamics in the 1D spinful Hubbard model. (a) After initializing a $T=1.4J$ thermal state with uniform Hamiltonian $U=1$, $t_{ij}=0.1$, the hopping $t_{ij}$ is adiabatically decreased with a spatial profile shown in the bottom part of the figure. The top part shows the change in the heat density as a function of time. (b) Depicts the onset of antiferromagnetic correlations. The rightmost site has a small Zeeman field $0.05S^z$. While the initial temperature disorders the spins, as the system cools, algebraic antiferromagnetic correlations clearly emerge.