Phase control of entanglement and quantum steering in a three-mode optomechanical system

Abstract

The theory of phase control of coherence, entanglement and quantum steering is developed for an optomechanical system composed of a single mode cavity containing a partially transmitting dielectric membrane and driven by short laser pulses. The membrane divides the cavity into two mutually coupled optomechanical cavities resulting in an effective three-mode closed loop system, two field modes of the two cavities and a mechanical mode representing the oscillating membrane. The closed loop in the coupling creates interfering channels which depend on the relative phase of the coupling strengths of the field modes to the mechanical mode. Populations and correlations of the output modes are calculated analytically and show several interesting phase dependent effects such as reversible population transfer from one field mode to the other, creation of collective modes, and induced coherence without induced emission. We find that these effects result from perfect mutual coherence between the field modes which is preserved even if one of the modes is not populated. The inseparability criterion for the output modes is also investigated and we find that entanglement may occur only between the field modes and the mechanical mode. We show that depending on the phase, the field modes can act on the mechanical mode collectively or individually resulting, respectively, in tripartite or bipartite entanglement. In addition, we examine the phase sensitivity of quantum steering of the mechanical mode by the field modes. Deterministic phase transfer of the steering from bipartite to collective is predicted and optimum steering corresponding to perfect EPR state can be achieved. These different types of quantum steering can be distinguished experimentally by measuring the coincidence rate between two detectors adjusted to collect photons of the output cavity modes. In particular, we find that the minima of the interference pattern of the coincidence rate signal the bipartite steering, while the maxima signal the collective steering. distant system, as considered in the original Einstein-Podolsky-Rosen (EPR) paradox [10]. The EPR steering allows two parties to verify the shared entanglement even if one measurement device is untrusted, which makes it an essential resource for one-sided device independent quantum cryptography [11][12][13][14][15][16], one-way quantum computing [17,18], secure quantum teleportation [19,20], and subchannel discrimination [21].Recent studies have revealed that coherence is closely related to entanglement and quantum steering. It was pointed out by Suzuki et al [22] that entanglement can be detected from interference fringes in atom-photon systems. It has also been shown that the coherence in a system and entanglement between that system and another initially incoherent one are quantitatively, or operationally, equivalent [23]. The power of quantum steering for the generation of coherence has also been demonstrated [24,25]. It has been shown that the presence of mutual coherence among two systems may have a ...

Manipulation and enhancement of asymmetric steering via interference effects induced by closed-loop coupling

“…In the following we will assume φ a = φ b = 0 and treat φ as the relative phase in the interference for simplicity. This coupling loop could be realized in three-mode optomechnical systems [48], or in antiferromagnets with magnon-photon coupling [58]. Substituting the Hamiltonian to the Heisenberg equation and taking into account the dissipation-fluctuation processes, we get the quantum Langevin equations (QLEs) for each modė…”

“…Finally, we have also demonstrated the opposite interference patterns of entanglement and steering between other pair of modes in the loop, indicating the monogamy constraints for distributing quantum correlations among multipartite. It is worth noticing that new quantum interference effects arising from a closed coupling loop have been recently applied to study optomechanical interferences and phonon correlations [47,48], the phase effects on phonon blockade effects [47,49], the transduction bandwidth of a rf-to-optical transducer [50], and the optical nonreciprocal behavior [51][52][53][54] which has been experimentally implemented [55][56][57].…”

Nonreciprocal transition between two nondegenerate energy levels

“…Based on a similar mechanism, many different schemes for nonreciprocal photon transport are proposed theoretically [5][6][7][8] and implemented experimentally [9][10][11][12]. Synthetic magnetism is an effective approach to achieve non-reciprocal transport of uncharged particles, such as photons [13][14][15][16] or phonons [17,18], for the potential applications in simulating quantummany-body phenomena [19][20][21][22][23][24][25], and creating devices robust against disorder and backscattering [26][27][28][29]. Reservoir engineering [30] has been a significant subject for generating useful quantum behavior by specially designing the couplings between a system of interest and a structured dissipative environment, such as cooling mechanical harmonic oscillators [31], synthesise quantum harmonic oscillator state [32], and generating state-dependent photon blockade [33], stable entanglement between two nanomechanical resonators [34,35], and squeezed states of nanomechanical resonators [36,37].…”

Few-photon optical diode in a chiral waveguide

“…It has to be stressed that the previous studies of optical nonreciprocity have mainly focused on transmission rates of the incident classical light. Very recently, nonreciprocal quantum effects have been explored theoretically [39], including nonreciprocal photon blockade [39][40][41][42][43][44] and nonreciprocal quantum entanglement [45,46], which open up a way to create and manipulate one-way nonclassical light.…”