The quantum/classical transition in mediated interactions

Abstract

Two quantum modes interacting via local couplings to a dissipative bosonic field are investigated theoretically. The model considers two mechanical modes with distinct frequencies coupled optomechanically to the same cavity mode. The dissipative cavity field mediates the interaction between the mechanical modes but also leads to decoherence of the mechanical oscillators. Depending on the ratio between effective interaction strength and dissipation rate, which can be chosen via the pump detuning, the interaction assumes a quantum mechanical or classical character. The distinction between the two regimes is made by the ability of the mediated interaction to correlate the two mechanical modes non-classically. For any cavity decay, there is a regime where the two mechanical modes interact in a nonclassical way, which leads us to conclude that optomechanical systems can serve as a model to experimentally study the transition of effective interactions mediated by classical or quantum-mechanical fields.The emergence of a classical world from quantum theories remains a challenge to our understanding of physics. One important mechanism through which microscopic interactions manifest themselves in macroscopic effects is long-range forces, such as the Coulomb interaction or gravitation. In microscopic descriptions, Lorentz invariance requires these forces to be the result of modes coupling locally to "force carriers", such as the photon or the hypothetical graviton. Tracing out the mediating fieldwhose excitations are referred to as "virtual" since they cannot be directly measured -yields the effective longrange interaction.According to a recently proposed model, two bodies experiencing an effective, non-local interaction mediated by a classical, rather than a quantum field, will experience additional random forces due to the carrier's inability to create non-classical correlations [1]. This additional noise causes the position variances of the two interacting modes to increase at a rate larger than twice the effective coupling strength. In Ref.[2], the same bound was found starting from a different model, where the description of a classically mediated non-local interaction was based on quantum measurement theory. A field mediating a non-local interaction is a channel carrying information about the participating bodies across space. The authors of [1,2] draw the line between classically and quantum-mechanically interacting bodies at the ability of the force-carrier to transfer quantum information. If, for example, one of the bodies is in a non-classical superposition state, a quantum mechanical force-carrier would faithfully convey this and -in the appropriate basis -also be in a superposition state. A classical channel, however, could not transfer this quantum information and thus must carry additional noise affecting both participating bodies. Besides the fundamental question of a possible quantum character of gravitation, the classicality of an interaction is of practical importance to technological applications of quan...

Cavity-mediated coupling of mechanical oscillators limited by quantum back-action

“…We observe the quantum back-action noise imparted by the optical coupling resulting in correlated mechanical fluctuations of the two oscillators. Our results illustrate challenges and opportunities of coupling quantum objects with light for applications of quantum cavity optomechanics [8][9][10][11][12][13][14] .…”

“…We observe the quantum back-action noise imparted by the optical coupling resulting in correlated mechanical fluctuations of the two oscillators. Our results illustrate challenges and opportunities of coupling quantum objects with light for applications of quantum cavity optomechanics [8][9][10][11][12][13][14] .Cavity optomechanical systems comprised of a single mechanical oscillator interacting with a single electromagnetic cavity mode 15 serve useful quantum-mechanical functions, such as generating squeezed light [16][17][18] , detecting forces with quantum-limited sensitivity 19 or through back-action-evading measurement 20 , and both entangling and amplifying mechanical and optical modes 21 . Systems containing several mechanical elements offer additional capabilities.…”

“…Systems containing several mechanical elements offer additional capabilities. In the quantum regime, these systems may enable two-mode back-action-evading measurements 9 , creation of nonclassical states 10 , fundamental tests of quantum mechanics 8,11,12 , correlations at the quantum level with applications in highsensitivity measurements 13 , and quantum information science 14 . Realizing these proposed functions requires multiple-element cavity optomechanical systems in which quantum-mechanical optical force fluctuations dominate over thermal and technical ones.…”

“…However, in such an optically driven system, the cavity photons not only mediate the two-way interaction, but also act as information carriers: The light emitted from the cavity permits measurements on the mechanical elements inside the cavity, leading to measurement back-action noise and limiting the capacity of cavity-mediated interactions to transfer quantum states between the coupled elements 8 . Thermal and technical noise prevented the observation of such incoherent back-action in previous optomechanical experiments.…”

“…This comparison implies that for the conditions of our experimentpump light detuned about one half-linewidth from the cavity resonance-the force linking the two mechanical oscillators cannot be used to exchange non-classical states of motion, such as phonon Fock states, between the oscillators. However, this limitation is not fundamental, and may be mitigated by driving the cavity further from its resonance frequency 8 -an effect similar to the avoidance of spontaneous emission on a far-detuned Raman transition-or through post-selection or feedback using light exiting the cavity.…”