Noninvasive measurement of dynamic correlation functions

Abstract

The measurement of dynamic correlation functions of quantum systems is complicated by measurement backaction. To facilitate such measurements we introduce a protocol, based on weak ancilla-system couplings, that is applicable to arbitrary (pseudo)spin systems and arbitrary equilibrium or nonequilibrium initial states. Different choices of the coupling operator give access to the real and imaginary parts of the dynamic correlation function. This protocol reduces disturbances due to the early time measurements to a minimum, and we quantify the deviation of the measured correlation functions from the theoretical, unitarily-evolved ones. Implementations of the protocol in trapped ions and other experimental platforms are discussed. For spin-1/2 models and single-site observables we prove that measurement backaction can be avoided altogether, allowing for the use of ancilla-free protocols.

Probing unitary two-time correlations in a neutral atom quantum simulator

“…In this section we briefly summarize the "ideal versions" (without taking into account imperfections and measurement noise) of the ancilla-free measurement protocols put forward in [11,12]. The protocols are applicable to arbitrary Hamiltonians H of interacting spin-1/2 degrees of freedom (qubits), on arbitrary lattices, and for arbitrary initial states.…”

“…As discussed in more detail in Refs. [11,12], the statistical error in Im C caused by the finite number of repetitions of the measurement is minimised for the choice of θ = ±π/2.…”

“…The shortcoming of these schemes is that they work only in specific settings, for specific initial states, and/or give access only to certain specific correlation functions. Another strategy for measuring two-time correlation functions consists in reducing the measurement backaction by making use of weak measurements (or generalised measurements, or quantum measurements), as proposed in [11,12]. While being applicable for very general Hamiltonians, initial states, and observables, the drawback of these protocols is that they require an exquisite control over the quantum system, and in particular the ability to temporarily couple auxiliary degrees of freedom to specific observables, as well as a large number of repetitions of the experiment in order to accumulate sufficient statistics.…”

“…In the same Refs. [11,12], a somewhat unexpected observation has been reported: for a certain class of Hamiltonians and observables, a projective measurement of the observable O 1 (t 1 ) at the earlier time t 1 has strictly no disturbing effect on the desired two-time correlation. This finding leads to a massive simplification compared to the above described weakmeasurement protocol: no auxiliary degrees of freedom are required, and the required number of repetitions of the experiment is orders of magnitude smaller.…”

“…In Sec. II we briefly summarize the ancilla-free measurement protocols (AFMP) for spin-1/2 lattices and single-site observables proposed in [11,12]. In Sec.…”