Quantum circuits for amplification of Kerr nonlinearity via quadrature squeezing

Abstract

Phase shifts induced by the Kerr effect are usually very small at the single-photon level. We propose two circuits for enhancing the cross-Kerr phase shift by applying one-and two-mode quadrature squeezing operators. Our results are based on the vector coherent state theory and can be implemented by physical operations satisfying the commutation relations for generators of the generalized special unitary group SU(1,1). While the proposed methods could be useful for the realization of quantum optical entangling gates based on Kerr nonlinear media at the single-photon level, they also indicate a general alternative approach to enhance higher-order nonlinearities by applying lowerorder nonlinear effects.

Cross-Kerr nonlinearity in optomechanical systems

“…In this case the refractive index associated with the propagation of one of the electric fields is changed with respect to the square amplitude of the other [15,16]. In quantum information, this effect plays an important role since it allows for creating entanglement between photons [17,18]. In the context of optomechanical systems, the cross-Kerr coupling between the resonator and the cavity induces a change in the refractive index of the cavity that depends on the number of phonons in the resonator, whereas the radiation -pressure coupling gives rise to an analogous effect that depends, however, on the displacement of the mechanical resonator.…”

Unconditional generation of bright coherent non-Gaussian light from exciton-polariton condensates

“…As a consequence, the occurrence of a negative Wigner function can be seen as a prerequisite for a potential quantum mechanical speed-up [13] (for related results on the discrete case, see [14]). While such negativities are necessary, even only small instances of it are sufficient for universality [13,15,16]. Unfortunately, since there are no media with strong enough nonlinearities, current experimental approaches to creating states with a negative Wigner function are highly probabilistic [17,18], only conditionally preparing such quantum states (those few deterministic schemes using solid-state emitters [19] would still not be capable of producing bright states).…”

Emission of photon pairs by mechanical stimulation of the squeezed vacuum

“…However, this squeezing also inputs thermal noise and two-photon correlation noise into the cavity. Although these undesired effects are negligible in the weak-squeezing case (see below), they can be completely eliminated by coupling a squeezed-vacuum bath, e.g., with a squeezing parameter r e and a reference phase θ e , to the a mode [50][51][52][53][54]. We assume that r e = r and θ e = ±nπ (n = 1, 3, 5, · · · ), so that the a s mode is equivalently coupled to a vacuum bath (see Appendix A).…”