Squeezed states of the electromagnetic field have been generated by nondegenerate four-wave mixing due to Na atoms in an optical cavity. The optical noise in the cavity, comprised of primarily vacuum fluctuations and a small component of spontaneous emission from the pumped Na atoms, is amplified in one quadrature of the optical field and deamplified in the other quadrature. These quadrature components are measured with a balanced homodyne detector. The total noise level in the deamplified quadrature drops below the vacuum noise level.

Observation of squeezed states generated by four-wave mixing in an optical cavity

A method is described to solve the nonlinear Langevin equations arising from quadratic interactions in quantum mechanics. While the zeroth order linearization approximation to the operators is normally used, here, first and second order truncation perturbation schemes are proposed. These schemes employ higher-order system operators, and then approximate number operators with their corresponding mean boson numbers only where needed. Spectral densities of higher-order operators are derived, and an expression for the second-order correlation function at zero time-delay has been found, which reveals that the cavity photon occupation of an ideal laser at threshold reaches 6 − 2 , in good agreement with extensive numerical calculations. As further applications, analysis of the quantum anharmonic oscillator, calculation of Q-functions, analysis of quantum limited amplifiers, and nondemoliton measurements are provided.

https://www.mdpi.com/2304-6732/4/4/48/pdf

Higher-Order Interactions in Quantum Optomechanics: Analytical Solution of Nonlinearity

We propose a scheme to generate remote asymmetric Einstein-Podolsky-Rosen (EPR) steering of two magnon modes in a hybrid ferromagnet-superconductor system. In our scheme, the indirect coherent coupling between two distant magnons and a $\mathrm{\ensuremath{\Delta}}$-type superconducting atom is established via exchange of virtual photons in two dispersive cavities. As a consequence, the artificial atom acting as a reservoir can produce asymmetrical magnon-magnon steering via a single dissipation channel. Interestingly, we find that the steering directivity is determined by cooling either Bogoliubov mode selectively rather than increasing the extra noise as in conventional schemes. This provides a novel idea to prepare remote EPR steering in solid devices, which may find potential applications in quantum information processing. 

/pdf/remote-asymmetric-einstein-podolsky-rosen-steering-of-2tpqbb6s.pdf

Remote asymmetric Einstein-Podolsky-Rosen steering of magnons via a single pathway of Bogoliubov dissipation

The success of quantum physics in description of various physical interaction phenomena relies primarily on the accuracy of analytical methods used. In quantum mechanics, many of such interactions such as those found in quantum optomechanics and quantum computing have a highly nonlinear nature, which makes their analysis extraordinarily difficult using classical schemes. Typically, modern quantum systems of interest nowadays come with four basic properties: (i) quantumness, (ii) openness, (iii) randomness, and (iv) nonlinearity. The newly introduced method of higher-order operators targets analytical solutions to such systems, and while providing at least mathematically approximate expressions with improved accuracy over the fully linearized schemes, some cases admit exact solutions. Many different applications of this method in quantum and classically nonlinear systems are demonstrated throughout. This review is purposed to provide the reader with ease of access to this recent and well-established operator algebra, while going over a moderate amount of literature review. The reader with basic knowledge of quantum mechanics and quantum noise theory should be able to start using this scheme to his or her own problem of interest.

Operator approach in nonlinear stochastic open quantum physics

We investigate the nonlinear optical response of a four-level double-V-type quantum system interacting with a pair of weak probe fields while located near a two-dimensional array of metal-coated dielectric nanospheres. Such a quantum system contains a V-type subsystem interacting with surface plasmons, and another V-type subsystem interacting with the free-space vacuum. A distinctive feature of the proposed setup is its sensitivity to the relative phase of the applied fields when placed near the plasmonic nanostructure. We demonstrate that due to the presence of the plasmonic nanostructure, the third-order (Kerr-type) susceptibility for one of the laser fields can be significantly modified while another probe field is acting. Moreover, the Kerr nonlinearity of the system can be controlled and even enhanced by varying the distance of the quantum system from the plasmonic nanostructure.We also show that the Kerr nonlinearity of such a system can be controlled by adjusting the relative phase of the applied fields. The results obtained may find potential applications in on-chip nanoscale photonic devices. We also study the light-matter interaction in the case where one probe field carries an optical vortex, and another probe field has no vortex. We demonstrate that due to the phase sensitivity of the closed-loop double V-type quantum system, the linear and nonlinear susceptibility of the nonvortex probe beam depends on the azimuthal angle and orbital angular momentum (OAM) of the vortex probe beam. This feature is missing in open four-level double V-type quantum system interacting with free-space vacuum, as no quantum interference occurs in this case. We use the azimuthal dependence of optical susceptibility of the quantum system to determine the regions of spatially-structured transmittance.

Spatially Structured Optical Effects in a Four-Level Quantum System Near a Plasmonic Nanostructure

We show that it is possible to obtain higher-order squeezing and entanglement between a pair of harmonic oscillators coupled to a single Δ-type artificial atom, which is realized because of the broken mirror symmetry of the effective potential in the superconducting circuits. Under the three-photon resonance and adiabatic conditions, the system can act as a coherence-controlled atomic reservoir, resulting in the generation of higher-order nonclassicality at steady state. The stable higher-order nonclassical correlations of the two harmonic oscillators in this solid-state device may find potential applications in quantum communications.

Higher-order squeezing and entanglement of harmonic oscillators in superconducting circuits

The transfer of optical vortices is studied based on double two-photon processes in a four-level diamond configuration system. A pair of strong fields are applied to prepare atomic coherence, while two weak probe fields are coupled with the other two transitions. When the two-photon resonances are satisfied, the analytical results for the intensities of the probe fields are calculated using perturbation theory and an adiabatic approximation approach. Our results explore whether the orbital angular momentum of an input probe beam or the second control field can be transferred to the generated probe field, and this is verified by numerical simulation. It is interesting that as the intensities of the control fields increase, the propagation of probe beams exhibits oscillation behaviors only when the one-photon detuning is nonzero. Furthermore, we show that the absorption losses are minimized, and the transfer efficiency is enhanced by appropriately modifying the one-photon detuning together with the control-field Rabi frequencies.

Transfer of optical vortices using two-photon processes in a diamond configuration atomic system

In this paper, we investigate the effects of incoherent pumping on quantum correlations in a Λ-type atomic system driven by coherent and incoherent fields simultaneously. With the adiabatic elimination treatment, we show that the stable “one-way” Einstein–Podolsky–Rosen (EPR) steering is generated without the requirement of good cavity limitation. More interestingly, the asymmetrical EPR steering is simply controlled by the polarized angle of the incoherent field. The internal mechanisms can be understood based on dressed-state representation, in which the population differences are strongly modified by the quantum interference from incoherent pumping. The phase-sensitive quantum correlations in the present scheme may find potential applications in quantum information processing.

Fei Wang

Papers

Higher-order squeezing and entanglement of harmonic oscillators in superconducting circuits

Transfer of optical vortices using two-photon processes in a diamond configuration atomic system

One-way Einstein–Podolsky–Rosen steering via quantum interference from incoherent pumping