Coherent-feedback-induced photon blockade and optical bistability by an optomechanical controller

It is well-known that some nonlinear phenomena such as strong photon blockade are hard to be observed in optomechanical system with current experimental technology. Here, we present a coherent feedback control strategy in which a linear cavity is coherently controlled by an optomechanical controller in a feedback manner. The coherent feedback loop transfers and enhances quantum nonlinearity from the controller to the controlled cavity, which makes it possible to observe strong nonlinear effects in either linear cavity or optomechanical cavity. More interestingly, we find that the strong photon blockade under single-photon optomechanical weak coupling condition could be observed in the quantum regime. Additionally, the coherent feedback loop leads to two-photon and multiphoton tunnelings for the controlled linear cavity, which are also typical quantum nonlinear phenomenon. We hope that our work can give new perspectives in engineering nonlinear quantum phenomena.Comment: 12 pages, 11 figure

Phononic Josephson oscillation and self-trapping with two-phonon exchange interaction

We propose a bosonic Josephson junction (BJJ) in two nonlinear mechanical resonator coupled through two-phonon exchange interaction induced by quadratic optomechanical couplings. The nonlinear dynamic equations and effective Hamiltonian are derived to describe behaviors of the BJJ. We show that the BJJ can work in two different dynamical regimes: Josephson oscillation and macroscopic self-trapping. The system can transfer from one regime to the other one when the self-interaction and asymmetric parameters exceed their critical values. We predict that a transition from Josephson oscillation to macroscopic self-trapping can be induced by the phonon damping in the asymmetric BJJs. Our results opens up a way to demonstrate BJJ with two-phonon exchange interaction and can be applied to other systems, such as the optical and microwave systems.Comment: 7 pages, 7 figure

Antibunching effect of the radiation field in a microcavity with a mirror undergoing heavily damping oscillation

The interaction between the radiation field in a microcavity with a mirror undergoing damping oscillation is investigated. Under the heavily damping cases, the mirror variables are adiabatically eliminated. The the stationary conditions of the system are discussed. The small fluctuation approximation around steady values is applied to analysis the antibunching effect of the cavity field. The antibunching condition is given under two limit cases.Comment: 5 pages, no figur

Mechanically modulated emission spectra and blockade of polaritons

We study a hybrid semiconductor-optomechanical system, which consists of a cavity with an oscillating mirror made by semiconducting materials or with a semiconducting membrane inside. The cavity photons and the excitons in the oscillating mirror or semiconducting membrane form into polaritons. And correspondingly, the optomechanical interaction between the cavity photons and the mirror or membrane is changed into the polariton-mechanical interaction. We theoretically study the eigenenergies and eigenfunctions of this tripartite hybrid system with the generalized rotating-wave approximation. We show that the emission spectrum of polariton mode is modulated by the mechanical resonator. We also study the mechanical effect on the statistical properties of the polariton when the cavity is driven by a weak classical field. This work provides a detailed description of the rich nonlinearity owing to the competition between parametric coupling and three-wave mixing interaction concerning the polariton modes and the phonon mode. It also offers a way to operate the photons, phonons and excitons, e.g., detect the properties of mechanical resonator through the fine spectra of the polaritons or control the transmission of light in the integrated semiconducting-optomechanical platform

Generating nonclassical photon-states via longitudinal couplings between superconducting qubits and microwave fields

Besides the conventional transverse couplings between superconducting qubits (SQs) and electromagnetic fields, there are additional longitudinal couplings when the inversion symmetry of the potential energies of the SQs is broken. We study nonclassical-state generation in a SQ which is driven by a classical field and coupled to a single-mode microwave field. We find that the classical field can induce transitions between two energy levels of the SQs, which either generate or annihilate, in a controllable way, different photon numbers of the cavity field. The effective Hamiltonians of these classical-field-assisted multiphoton processes of the single-mode cavity field are very similar to those for cold ions, confined to a coaxial RF-ion trap and driven by a classical field. We show that arbitrary superpositions of Fock states can be more efficiently generated using these controllable multiphoton transitions, in contrast to the single-photon resonant transition when there is only a SQ-field transverse coupling. The experimental feasibility for different SQs is also discussed.Comment: 15 pages, 8 figure

Backlund transformations for Burgers Equation via localization of residual symmetries

In this paper, we obtained the non-local residual symmetry related to truncated Painlev\'e expansion of Burgers equation. In order to localize the residual symmetry, we introduced new variables to prolong the original Burgers equation into a new system. By using Lie's first theorem, we got the finite transformation for the localized residual symmetry. More importantly, we also localized the linear superposition of multiple residual symmetries to find the corresponding finite transformations. It is interesting to find that the nth Backlund transformation for Burgers equation can be expressed by determinants in a compact way

Single-photon nonreciprocal transport in one-dimensional coupled-resonator waveguides

We study the transport of a single photon in two coupled one-dimensional semi-infinite coupled-resonator waveguides (CRWs), in which both end sides are coupled to a dissipative cavity. We demonstrate that a single photon can transfer from one semi-infinite CRW to the other nonreciprocally. Based on such nonreciprocity, we further construct a three-port single-photon circulator by a T-shaped waveguide, in which three semi-infinite CRWs are pairwise mutually coupled to each other. The single-photon nonreciprocal transport is induced by the breaking of the time-reversal symmetry and the optimal conditions for these phenomena are obtained analytically. The CRWs with broken time-reversal symmetry will open up a kind of quantum devices with versatile applications in quantum networks.Comment: 10 pages, 6 figure

Nonreciprocal conversion between microwave and optical photons in electro-optomechanical systems

We propose to demonstrate nonreciprocal conversion between microwave and optical photons in an electro-optomechanical system where a microwave mode and an optical mode are coupled indirectly via two non-degenerate mechanical modes. The nonreciprocal conversion is obtained in the broken time-reversal symmetry regime, where the conversion of photons from one frequency to the other is enhanced for constructive quantum interference while the conversion in the reversal direction is suppressed due to destructive quantum interference. It is interesting that the nonreciprocal response between the microwave and optical modes in the electro-optomechanical system appears at two different frequencies with opposite directions. The proposal can be used to realize nonreciprocal conversion between photons of any two distinctive modes with different frequencies. Moreover, the electro-optomechanical system can also be used to construct a three-port circulator for three optical modes with distinctively different frequencies by adding an auxiliary optical mode coupled to one of the mechanical modes.Comment: 10 pages, 4 figure

Tunable Electromagnetically Induced Transparency and Absorption with Dressed Superconducting Qubits

Electromagnetically induced transparency and absorption (EIT and EIA) are usually demonstrated by three-level atomic or atom-like systems. In contrast to the usual case, we theoretically study the EIT and EIA in an equivalent three-level system, which is constructed by dressing a superconducting two-level system (qubit) dressed by a single-mode cavity field. In this equivalent system, we find that both the EIT and the EIA can be tuned by controlling the level-spacing of the superconducting qubit and hence controlling the dressed system. This tunability is due to the dressed relaxation and dephasing rates which vary parametrically with the level-spacing of the original qubit and thus affect the transition properties of the dressed qubit and the susceptibility. These dressed relaxation and dephasing rates characterize the reaction of the dressed qubit to an incident probe field. We also use recent experimental data on superconducting qubits (charge, phase, and flux qubits) to demonstrate our approach and show the possibility of experimentally realizing this proposal.Comment: 13 page

New interaction solutions of Kadomtsev-Petviashvili equation

The residual symmetry coming from truncated Painleve expansion of KP equation is nonlocal, which is localized in this paper by introducing multiple new dependent variables. By using the standard Lie group approach, the symmetry reduction solutions for KP equation is obtained based on the general form of Lie point symmetry for the prolonged system. In this way, the interaction solutions between solitons and background waves is obtained, which is hard to study by other traditional methods