PHASE-SENSITIVE BACK-ACTION ON A MICROSCOPIC SYSTEM

Vittorio Bagini, P B Lerner, Paolo Tombesi

Vladimir B. Braginsky, Farid Ya Khalili, Kip S. Thorne

Fluctuational and dynamical back action of the measuring device During a continuous monitoring of a quantum object, the measuring device can act back on the object in general in two different ways: First, it can influence the evolution of the expectation value of the measured observables. This is called the “dynamical back action,” and it is a regular, predictable effect. (An example is the dynamical back action produced by the dynamical rigidity of a capacity sensor, which will be discussed in chapter X.) Second, the measuring device can perturb the observables in a random way, increasing their uncertainties, i.e. producing random deviations from their expectation values. A key feature of linear, continuous measurements, as discussed in the last chapter, is that for them these two types of back action are completely independent. The fluctuational back action is fundamental and irremovable, while the dynamical back action can be avoided entirely by a suitable construction of the measuring device. For nonlinear systems the situation is completely different, as one can readily see from a typical example of a nonlinear, continuous measurement: a monitoring of an oscillator's energy. In accord with the uncertainty relation, the energy measurement produces perturbations of the oscillator's phase, and as the measurement proceeds continuously, these perturbations cause the phase to diffuse in a Brownian-motion type way.

Takashi Nakajima, P. Lambropoulos

Lech S. Papiez

Tomonori Matsushita, Holger Friedrich Hofmann

Information about the internal properties of a system can only be obtained through interactions of the system with an external meter. However, such interactions generally result in entanglement between the system and the meter, making it difficult to trace the measurement result back to a specific value of the physical property in the system. It is therefore possible that the outcomes of quantum measurements depend in a nontrivial manner on the dynamics of the measurement interaction, possibly providing a physical explanation for the role of measurement contexts in quantum mechanics. Here we show that the effects of the measurement interaction on the meter can be described entirely in terms of the quantum coherent system dynamics associated with the back-action on the system. For sufficiently small back-action uncertainties, the physical property of the system is described by a weak value obtained from the Hamilton-Jacobi equation of the back-action dynamics. At higher measurement resolutions, the observed values are determined by quantum interferences between different amounts of back-action. Eigenvalues emerge when the quantum interferences between different back-actions correspond to a Fourier transform in the back-action parameter. We conclude that the values of physical properties obtained in quantum measurements originate from the quantum coherent properties of the back-action dynamics generated by that physical property during an interaction. Measurement outcomes represent elements of the dynamics and cannot be explained by measurement independent elements of reality.

Juha Javanainen, Janne Ruostekoski

We develop a classical theoretical description for nonlinear many-body dynamics that incorporates the back-action of a continuous measurement process. The classical approach is compared with the exact quantum solution in an example with an atomic Bose–Einstein condensate in a double-well potential where the atom numbers in both potential wells are monitored by light scattering. In the classical description, the back-action of the measurements appears as diffusion of the relative phase of the condensates on each side of the trap. When the measurements are frequent enough to resolve the system dynamics, the system behaves classically. This happens even deep in the quantum regime, and demonstrates how classical physics emerges from quantum mechanics as a result of measurement back-action.