Interaction of squeezed states with nonlinear optical systems

Ali Dalafi, M. H. Naderi, M. Soltanolkotabi

In this paper, we investigate theoretically a system consisting of a one dimensional Bose-Einstein condensate trapped inside the optical lattice of an optical cavity. In the weak-interaction regime and under the Bogoliubov approximation, the wave function of the Bose-Einstein condensate can be described by a classical field (condensate mode) having some quantum fluctuations (the Bogoliubov mode) about the mean value. Such a system behaves as a so-called atomic parametric amplifier, similar to an optical parametric amplifier, where the condensate and the Bogoliubov modes play respectively, the roles of the pump field and the signal mode in the degenerate parametric amplifier and the s-wave scattering frequency of atom-atom interaction plays the role of the nonlinear gain parameter. We show that using the nonlinear effect of atomic collisions, how one can manipulate and control the state of the Bogoliubov mode and produce squeezed states.

Faige F. Singer

Houcem Jabri, Hichem Eleuch

We investigate a hybrid system consisting of an optomechanical resonator and an optical cavity containing a quantum well. The system is coupled to a squeezed vacuum reservoir. We analyze the effect of the injection of squeezed photons inside the cavity on the intensity spectrum. The system reaches a regime of hybrid resonance where mechanical, excitonic and cavity modes are intermixed. Despite that the optomechanical interaction is the source of the nonlinearity in the system, the optimum squeezing is obtained at the hybrid resonance frequencies. However, when the squeezed vacuum is applied, at these frequencies the minimum squeezing is realized as well as an increase of fluctuations is observed. We show that the squeezed vacuum transforms the coherent states into highly squeezed states of light, and offers a great flexibility to obtain maximal squeezing. Furthermore, a perfect squeezing is predicted.

Sofia Arranz Regidor, Matthew Kozma, Stephen Hughes

Squeezed light states have a special place in quantum optics with potentially profound applications in emerging quantum technologies. We present a numerically-exact matrix product states (MPS) approach to model quantum pulses of squeezed light, at the few-photon level, interacting with a two-level system in a waveguide environment. We represent the squeezed state as a coherent superposition of Fock states and explore the nonlinear population dynamics as well as multi-photon correlation functions that emerge. We show how the squeezed pulse can create quantum correlations that are unique to squeezed pulses, including $\langle b(t) b(t+t')\rangle$ for transmitted fields as well as $\langle b^\dagger(t) b^\dagger(t+t') b(t+t') b(t) \rangle$. We also demonstrate how $\langle b(t) b(t+t') \rangle$, a first-order correlation function, shows nonlinear photon correlations that are similar to those known and measured for two-photon scattering states. Finally, we also study the squeezed spectra of the pulse before and after interacting with the two-level system, and highlight the role of the spectral bandwidth of the incident pulse. The MPS theory allows the modeling of arbitrary bandwidth squeezing without making any Markov and Born approximations for the light-matter interaction processes, and can easily be extended to waveguide systems with multiple emitters and time-delayed feedback.

David A. Holm, M. Sargent, Barbara A. Capron

Carlton M. Caves