Measurement Quench in Many-Body Systems

Measurement is one of the key concepts which discriminates classical and quantum physics. Unlike classical systems, a measurement on a quantum system typically alters it drastically as a result of wave function collapse. Here we suggest that this feature can be exploited for inducing quench dynamics in a many-body system while leaving its Hamiltonian unchanged. Importantly, by doing away with dedicated macroscopic devices for inducing a quench—using instead the indispensable measurement apparatus only—the protocol is expected to be easier to implement and more resilient against decoherence. By way of various case studies, we show that our scheme also has decisive advantages beyond reducing decoherence—for spectroscopy purposes and probing nonequilibrium scaling of critical and quantum impurity many-body systems.

Figure 1

Measurement quench. A local measurement is performed on one of the qubits of a chain prepared in its ground state. This causes a collapse to a new state and induces dynamics in the system.

Figure 2

Transverse field Ising chain with long-range interaction. The magnetization $m_1^x(t)$ as a function of time in a chain of length $N=20$ and $B/J=1$ for two types of long-range interaction: (a) $\alpha =0.5$; (b) $\alpha =3$. The insets show the Fourier transform $M_1^x(E)$ as function of energy $E$ for the chosen value of $\alpha$.

Figure 3

Magnetization dynamics in the transverse field Ising chain. Time evolution of the local magnetization after a measurement quench in the Ising model for (a) $\lambda =0.95$, and (b) $\lambda ={\lambda }_c=1$. Nonequilibrium scaling of the local magnetization $m_j^x$ versus $t/N$ for (c) $|\lambda -{\lambda }_c|\simeq 1/N$ and (d) $|\lambda -{\lambda }_c|=0$, for which all lengths behave in the same way since $\xi \sim N$.

Figure 4

Magnetization dynamics in the Kondo model. Nonequilibrium scaling of the local magnetization $m_1^x$ versus $t/N$ when the length scale ${\xi }_K$ is tuned to (a) $N/{\xi }_K\simeq 3.4$, (b) $N/{\xi }_K\simeq 2$.

Figure 5

Detecting the Kondo cloud. (a) Average local magnetization difference ${\overline{\mathrm{\Delta }m}}_j$ as a function of measurement site $j$ in a chain of $N=32$ and $J^{\prime }=0.3$. (b) The length scale ${\xi }_K$ versus $1/J^{\prime }$ for the chain of length $N=32$ and $J^{\prime }=0.3$. The semilogarithmic plot confirms its exponential dependence with the fitting parameter $A=0.18$.