Polaron formation in a spin chain by measurement-induced imaginary Zeeman field

We present a high-rate projective measurement-based approach for controlling nonunitary evolution of a quantum chain of interacting spins. In this approach, we demonstrate that local measurement of a single external spin coupled to the chain can produce a spin polaron, which remains stable after the end of the measurement. This stability results from the fact that the Hilbert space of the chain contains a subspace of nondecaying states, stable during the nonunitary evolution. These states determine the resulting final state of the chain and long-term shape of the polaron. In addition to formation of the spin polarons, the presented measurement protocol can be used for distillation of nondecaying states from an initial superposition or mixture.

Figure 1

Schematic picture of a spin chain with locally connected probe (dark blue circle) being under frequent selective measurements. The measurements are performed at times $t=k\tau ,$ where $k$ is an integer. Red arrows correspond to the in-plane components of the spins, and the sizes of the blue circles correspond to their $Z$ components.

Figure 2

(a) Numerically estimated survival probability ${\overline{P}}_{\infty }$ as a function of spin number $N$. (b) Dimension of nondecaying subspace vs the number of spin which probe coupled with for an open chain with $N=7$.

Figure 3

Survival probability $P$ as a function of time for the first four eigenstates as initial states of the spin chain with $N=6, \tau =0.03$, and $g=4$.

Figure 4

Example of magnetization dynamics for the spin chain with $N=6, \tau =0.03$. (a) $g=4$, and the probe spin is disconnected at $t=12$ (vertical line). (b) $g=0.5$, and the probe is not disconnected. Numeration of spins corresponds to Fig. 1.

Figure 5

Averaged local magnetization from the ensemble of 100 random initial states. The probe spin disconnected at $t=9$ (vertical line), and after this time, spin chain evolution is governed by Hamiltonian (1).

Figure 6

Averaged local magnetization from the ensemble of 100 random initial states in the form $|{\psi }_0\rangle ={|\uparrow \rangle }_1\otimes |\mathrm{Random}\mathrm{state}\rangle$.

Figure 7

Distillation of a nondecaying state $|\Uparrow \rangle$ from initial superposition $|{\psi }_0\rangle ={(|\mathrm{GS}\rangle +a|\Uparrow \rangle )(1+|a|}^2{)}^{-1/2}$.