Evading Quantum Mechanics: Engineering a Classical Subsystem within a Quantum Environment

Abstract

Quantum mechanics is potentially advantageous for certain information-processing tasks, but its probabilistic nature and requirement of measurement backaction often limit the precision of conventional classical information-processing devices, such as sensors and atomic clocks. Here we show that, by engineering the dynamics of coupled quantum systems, it is possible to construct a subsystem that evades the measurement backaction of quantum mechanics, at all times of interest, and obeys any classical dynamics, linear or nonlinear, that we choose. We call such a system a quantum-mechanics-free subsystem (QMFS). All of the observables of a QMFS are quantum-nondemolition (QND) observables; moreover, they are dynamical QND observables, thus demolishing the widely held belief that QND observables are constants of motion. QMFSs point to a new strategy for designing classical information-processing devices in regimes where quantum noise is detrimental, unifying previous approaches that employ QND observables, backaction evasion, and quantum noise cancellation. Potential applications include gravitational-wave detection, optomechanical-force sensing, atomic magnetometry, and classical computing. Demonstrations of dynamical QMFSs include the generation of broadband squeezed light for use in interferometric gravitational-wave detection, experiments using entangled atomic-spin ensembles, and implementations of the quantum Toffoli gate. According to quantum mechanics, a measurement of the position of an object must introduce uncertainty to its momentum, called the measurement backaction noise. Since position is coupled to momentum, as the object evolves in time, the backaction noise can perturb the position and contaminate subsequent position measurements. Scientists studying gravitational-wave detection, concerned that this dynamical effect of measurement backaction would place a fundamental limit to the detectors, proposed a general solution: If a quantum observable, represented by a self-adjoint operator OðtÞ in the Heisenberg picture, can be made to commute with itself at times t and t 0 when the observable is measured, viz.,then O can be measured repeatedly with no quantum limits on the predictability of these measurements. In particular, this means that quantum mechanics does not limit the detection of a classical signal that affects O.An observable that obeys Eq. (1) (1) is satisfied, the conjugate observables do not feed back onto the QND observable at the times of interest.The most well-known QND observables are ones that remain static in the absence of classical signals, viz.,

Macroscopic quantum mechanics: theory and experimental concepts of optomechanics

“…Further theoretical developments in this direction of research includes the characterization of the maximal amount of information extractable from a system by a measuring device, and the best observable of the system to measure in order to extract a certain type of information [9,10,11,12,13]. In the field of gravitational-wave detection, a program exploring laser interferometer configurations that can best achieve sub-SQL sensitivity is being pursued, both theoretically and experimentally [14,15,16,17].…”

Quantum Backaction Evading Measurement of Collective Mechanical Modes

“…BAE techniques have previously been discussed for two coupled mechanical oscillators [16] and optomechanical systems [17,18], and demonstrated for two atomic spin ensembles [19]. In a recent theoretical work [20], the concept has been extended to the collective modes of two uncoupled mechanical oscillators, each independently coupled to an electromagnetic cavity.…”

“…Under this Hamiltonian, X þ and P − act dynamically like the position and momentum of a single harmonic oscillator, even though they commute with one another [18,20,38]. It is an example of the recently introduced concept of a "quantum-mechanics-free subsystem" [18], previously observed in an atomic system [19]. Only the X þ collective quadrature couples to the cavity, and is measured by observing the cavity output.…”

Room-Temperature Steady-State Entanglement in a Four-Mode Optomechanical System

“…space [28][29][30]. We can have a special form − + δY 2 + < 1, the two target modes can be entangled according to the criterion in [34].…”

“…The situation that the two optomechanical couplings between the two target modes and the mechanical oscillator are equal can not be explained by the Bogoliubov-mode-based scheme [16]. This is connected with the ideas of quantum-mechanicsfree subspace [28][29][30]. The mechanical thermal noise effect is discussed.…”