cross-Kerr Effect Research Articles

Microwave optical limiting via an acoustic field in a diamond mechanical resonator.

We investigate the generation and control of the reverse saturable absorption (RSA) and optical limiting (OL) at microwave (mw) range in high-Q single-crystal diamond mechanical resonator (DMR) embedded with many nitrogen-vacancy (NV) centers. The strain-induced acoustic modes enable mechanical manipulation of NV centers. On the basis of strain-coupling mechanism, it is shown that the saturable absorption (SA) switches to the RSA by applying the acoustic field, leading to induce the OL in the diamond through the cross-Kerr effect. We demonstrate that the OL characteristics such as, threshold, efficiency, and dynamic range can be controlled by changing either the intensity or frequency of the acoustic field. Moreover, we show that this optical limiter can amplify noiselessly the low intensity of the mw field input to the sensors and also attenuate any gain-induced noise and increase in the intensity of the mw field if it exceeds the intensity threshold. In addition, it is shown that by increasing either the number of NV centers or length of the diamond, the optical limiter can be more efficient. The physical mechanism of the OL establishment is explained using the analytical expressions, which are in good agreement with the numerical results. Our proposed acoustic-induced optical limiter can be a scheme for protecting different optical and electronic devices in mw range, remote sensing, navigation, communications, microwave heating and thermo/laser therapy.

Effects of cross-Kerr coupling on transmission spectrum of double-cavity optomechanical system

We theoretically study the transmission spectrum of the cavity field in a double-cavity optomechanical system with cross-Kerr (CK) effect. The system consists of two tunneling coupling optomechanical cavities with a mechanical resonator as a coupling interface. By doping CK medium into the mechanical resonator, CK couplings between the cavity fields and the mechanical resonator are introduced. We investigate the effects of CK coupling strength on the transmission spectrum of the cavity field, including the transmission rate, nonreciprocity and four-wave mixing (FWM). We find that the transmission spectrum of the probe field can show two obvious transparent windows, which can be widened by increasing the CK coupling strength. For the transmission between the two cavity fields, the perfect nonreciprocity and reciprocity are present and modulated by CK coupling and phase difference between two effective optomechanical couplings. In addition, the effects of the optomechanical and CK couplings on FWM show that the single peak of FWM is split into three symmetrical peaks due to the introduction of the CK effect.

Control over magneto-optical plasmon rotation with Doppler broadening and cross-Kerr non-linearity

We investigate the impacts of cross-Kerr non-linearity and Doppler broadening on the magneto-optical rotation (MOR) induced in surface plasmon polaritons (SPPs) located at the interface of a metalic medium and a 4-level atomic system. In this paper, the external static magnetic field and a weak probe field under the cross-Kerr effect result in the birefringence enhancement of the system. Moreover, the incoherent effect of Doppler broadening can regulate the MOR of SPPs. Notably, the controlled MOR of SPPs can be leveraged for a variety of advantageous implementations in the fields of polarization spectroscopy, optical communication, nanoscale Faraday isolation, accurate metrology, as well as bio/chem sensing technologies.

Influence of pump brightness, self-Kerr and cross-Kerr effects on the entanglement of partially degenerate triple-photon state

Recently, partially degenerate triple-photon states (TPS) generated by the third-order spontaneous parametric down-conversion have been observed in a superconducting cavity (2020, Phys. Rev. X 10, 011011). Their non-Gaussian entanglement properties, characterized by a series of high-order covariance matrices, have also been theoretically revealed. Here, we use the non-Gaussian entanglement criterion proposed in (2021, Phy. Rev. Lett. 127, 150502) and the logarithmic negativity to study the effect of pump brightness, self-Kerr and cross-Kerr interactions on the entanglement of partially degenerate TPS (PDTPS). We find that the brighter the pump, the easier the entanglement of PDTPS leap to higher-order covariance matrices. Although both self-Kerr and cross-Kerr interactions induce nonlinear phase shifts and weaken the entanglement of PDTPS, cross-Kerr interactions can effectively raise the threshold of entanglement loaded on the third-order covariance matrix. These results can contribute to our understanding of the mechanism of the generation of unconditional non-Gaussian entanglement.

Modulating Airy vortex beam by Kerr nonlinear effect

The modulation of Airy vortex beam by electromagnetically induced transparency (EIT) effect and Kerr nonlinear effect is studied theoretically and experimentally. We introduce the vortex to Airy beam through the interference between the lobes of Airy beam for the first time. The formation and disappearance of the vortex can be modulated by the EIT effect. Also, the interference between the main lobe and side lobes leads to the energy redistribution of the Airy beam. We have found that with the change of the power and frequency detuning of the dressing field, the lobes of Airy beam will shift spatially due to the cross-Kerr effect. At the two-photon resonance point, the shift reaches its maximum. In addition, defocusing and focusing caused by self-Kerr effect happen in the lobes. Overall, the regulation of Airy vortex beam we have achieved by multi-parameters will play a significant part in the realm of complex optical micro-manipulation.

Single photons versus coherent-state input in waveguide quantum electrodynamics: Light scattering, Kerr, and cross-Kerr effect

While the theoretical studies in waveguide quantum electrodynamics predominate with single-photon and two-photon Fock-state (photon number states) input, the experiments are primarily carried out using a faint coherent light. We create a theoretical toolbox to compare and contrast linear and nonlinear light scattering by a two-level or a three-level emitter embedded in an open waveguide carrying Fock-state or coherent-state inputs. We particularly investigate light transport properties and the Kerr and cross-Kerr nonlinearities of the medium for the two types of inputs. A generalized description of the Kerr and cross-Kerr effect for different types of inputs is formulated using the first-order correlation function to compare the Kerr and cross-Kerr nonlinearity between two photons in these models.

Spatially structured multi-wave-mixing induced nonlinear absorption and gain in a semiconductor quantum well

We have studied two-dimensional absorption and gain spectrum in an asymmetric semiconductor triple-coupled-quantum-well (TCQW) nanostructure. Four subband transitions are coupled by using four coherent fields in a close-loop configuration to introduce cross-Kerr effect and four-wave-mixing (FWM) induced nonlinearity in achieving nonlinear absorption and gain profiles. Position-dependent absorption and gain are obtained by applying one, or two coherent fields in a variety of standing wave configurations including superposed field configuration in the standing-wave regime. In addition to the control parameters like Rabi frequency and detuning, the specialty of the model is to employ double-controlled spatial phase-coherence guided by the FWM-induced phase and the phases introduced by the standing wave formation. Our results highlight the high-precision electron localization in spatial domain. The evolution of spatially modulated gain without inversion may be a substitute for obtaining gain from a traditional quantum cascade laser. The importance of the present work is to find its application in designing electro-optic modulators in semiconductor nanostructures in near future.

Simultaneous ground-state cooling of multiple degenerate mechanical modes through the cross-Kerr effect.

Simultaneous ground-state cooling of multiple degenerate mechanical modes is a difficult issue in optomechanical systems, owing to the existence of the dark mode effect. Here we propose a universal and scalable method to break the dark mode effect of two degenerate mechanical modes by introducing cross-Kerr (CK) nonlinearity. At most, four stable steady states can be achieved in our scheme in the presence of the CK effect, unlike the bistable behavior of the standard optomechanical system. Under a constant input laser power, the effective detuning and mechanical resonant frequency can be modulated by the CK nonlinearity, resulting in an optimal CK coupling strength for cooling. Similarly, there will be an optimal input laser power for cooling when the CK coupling strength stays fixed. Our scheme can be extended to break the dark mode effect of multiple degenerate mechanical modes by introducing more than one CK effect. To fulfill the requirement of the simultaneous ground-state cooling of N multiple degenerate mechanical modes, N - 1 CK effects with different strengths are needed. Our proposal provides new, to the best of our knowledge. insights into dark mode control and might pave the way to manipulating multiple quantum states in a macroscopic system.

Electrically controlled optical nonlinear effects in the hybrid opto-electromechanical system with the cross-Kerr effect

We theoretically study the nonlinear optical phenomena including optical stability state and four-wave mixing (FWM) process in a hybrid opto-electromechanical system with the cross-Kerr (CK) effect. The hybrid system consists of an optomechanical cavity in which the cross-Kerr (CK) effect and Coulomb interaction are simultaneously introduced by the CK medium and the mechanical resonator capacitively coupling to an external circuit, respectively. The CK interaction induces a tristability behavior of the mean intracavity photon number, which can be modulated by the strength of the CK effect and electrically controlled by the voltage on the capacitor. In addition, we give the effects of the optomechanical, CK, and Coulomb coupling strengths on the FWM of the output field. The results show that the voltage can be employed to electrically engineer the optical nonlinear phenomena.

An analytical model for cross-Kerr nonlinearity in a four-level N-type atomic system with Doppler broadening

We present an analytical model for cross-Kerr nonlinear coefficient in a four-level N-type atomic medium under Doppler broadening. The model is applied to 87Rb atoms to analyze the dependence of the cross-Kerr nonlinear coefficient on the external light field and the temperature of atomic vapor. The analysis shows that in the absence of electromagnetically induced transparency (EIT) the cross-Kerr nonlinear coefficient is zero, but it is significantly enhanced when the EIT is established. It means that the cross-Kerr effect can be turned on/off when the external light field is on or off. Simultaneously, the amplitude and the sign of the cross-Kerr nonlinear coefficient are easily changed according to the intensity and frequency of the external light field. The amplitude of the cross-Kerr nonlinear coefficient remarkably decreases when the temperature of atomic medium increases. The analytical model can be convenient to fit experimental observations and applied to photonic devices.

Laguerre-Gaussian modes generated vector beam via nonlinear magneto-optical rotation

Laguerre-Gaussian (LG) beams contain a helical phase front with a doughnut-like intensity profile. We use the LG beam to introduce a rather simple method for generation of a vector beam (VB), a beam with spatially-dependent polarization in the beam cross section, via the nonlinear magneto-optical rotation (NMOR). We consider the NMOR of the polarization of a linearly polarized probe field passing through an inverted Y-type four-level quantum system interacting with a LG control field and a static magnetic field. It is shown that the polarization of the transmitted field is spatially distributed by the orbital angular momentum (OAM) of the LG control field, leading to generation of the VB with azimuthally symmetric polarization distribution. We show that the polarization and intensity distributions of the VB spatially vary by changing the OAMs of the LG control field. Moreover, the radial index of the LG control field has a major role in more spatially polarization distributing of the VB. It is shown that the intensity of the generated VBs in different points of the beam cross section can be controlled by the OAM as well as the radial index of the LG control field. However, the VB with highly spatially distributed can be generated for higher values of the radial index of LG control field. The analytical calculations determine the contribution of the different nonlinear (cross-Kerr effect) phenomena on the generation of the VB. We show that the VB is mainly generated via birefringence induced by the applied fields. Finally, we use asymmetric LG (aLG) beams for making the VBs with asymmetric polarization distribution. It is shown that by applying aLG beams, the azimuthal symmetry of the polarization distribution breaks and the asymmetric polarization distribution can be controlled by OAM and radial index of the aLG control field. The obtained results may find more interesting applications in fiber/free space optical communication to enhance the capacity of the information transmission.

Acoustic field induced nonlinear magneto-optical rotation in a diamond mechanical resonator

We study the nonlinear magneto-optical rotation (MOR) of a linearly polarized microwave probe field passing through many nitrogen-vacancy (NV) centers embedded in a high-Q single-crystal diamond mechanical resonator. On the basis of the strain-mediated coupling mechanism, we establish a three-level closed-loop system in the ground states of the NV center in the presence of a static magnetic field. It is shown that by applying an acoustic field, the birefringence is induced in the system through the cross-Kerr effect, so that the probe field is transmitted with a high intensity and rotated polarization plane by 90 degrees. In addition, we demonstrate that the acoustic field has a major role in enhancing the MOR angle to 90 degrees. Moreover, it is shown that the MOR angle of the polarization plane after passing through the presented system is sensitive to the relative phase of the applied fields. The physical mechanism of the MOR enhancement is explained using the analytical expressions which are in good agreement with the numerical results. The presented scheme can be used as a polarization converter for efficient switching TE/TM modes in optical communication, the depolarization backscattering lidar, polarization spectroscopy and precision measurements.

Quantum Versus Classical Switching Dynamics of Driven Dissipative Kerr Resonators

We report a first-principles study of the driven dissipative dynamics for Kerr oscillators in the mesoscopic regime. This regime is characterized by large Kerr nonlinearity, realized here using the nonlinear kinetic inductance of a large array of Josephson junctions. The experimentally measured nonlinear resonance lineshapes of the junction array modes show significant deviations from steady-state numerical predictions, and necessitate time-dependent numerical simulations indicative of strong measurement-induced dephasing in the system arising from the large cross-Kerr effect between array modes. Analytical and numerical calculations of switching rate corroborate this by showing the emergence of a slow time scale, which is much longer than the linear decay rate and is set by fluctuation-induced switching times in the bistable regime. Furthermore, our analysis shows that the usual quantum-activated escape treatment is inadequate for prediction of the switching rates at large frequency shifts caused by strong nonlinearities, necessitating a quantum treatment that utilizes the full system Liouvillian. Based on our analysis, we identify a universal crossover parameter that delineates the regimes of validity of semiclassical and quantum descriptions, respectively. Our work shows how dynamical switching effects in strongly nonlinear systems provide a platform to study quantum-to-classical transitions.

Control of light in a quantized four level graphene atomic system via self and cross-Kerr nonlinearity

Abstract We investigate self and cross-Kerr nonlinearity in a four level quantized graphene atomic medium. The absorption, dispersion, transmission and subluminal/superluminal behaviors of a probe light field are studied. An amplification of the probe light field is observed in the absorption spectrum. The normal and anomalous slope of dispersion is also investigated at the positive/negative absorption region. It is shown that Kerr nonlinearity invert and enhance the subluminal/superluminal behaviors of the pulse and self-Kerr effect is found to be more subluminal/superluminal as compared to cross-Kerr effect. The results show significant applications in information storage, self and cross phase modulation and lasing without inversion.

Dressed optical vortex in a hot atomic medium

We experimentally observe the vortex six-wave mixing (SWM) signal carrying orbital angular momentum in a photonic band gap structure. First, we scan the probe detuning and the detuning of the dressing field to find an explanation for the intensity variation of four-wave mixing (FWM) intensity and the shift of forks in interference patterns. Then we change the power of the coupling field and obtain SWM images as well as its interference patterns to investigate the propagation characteristics, including spatial shift and splitting. We observe a change of fork quantity when decreasing the incident angle of the probe field. We suppose that the reflected signal is a combination of a linear probe and a nonlinear vortex FWM signal. By changing the incident angle of the field, the overlap condition between fields have changed correspondingly and the cross-Kerr effect of the coupling field on the linear vortex probe and third-order FWM become different, causing a separation in the center of the two components, which brings the inducement of additional forks.

Quantum Behavior of a PT -Symmetric Two-Mode System with Cross-Kerr Nonlinearity

Quantum behavior of two oscillator modes, with mutually balanced gain and loss and coupled via linear coupling (including energy conserving as well as energy non-conserving terms) and nonlinear cross-Kerr effect, is investigated. Stationary states are found and their stability analysis is given. Exceptional points for PT -symmetric cases are identified. Quantum dynamics treated by the model of linear operator corrections to a classical solution reveals nonclassical properties of individual modes (squeezing) as well as their entanglement.

Cross-Kerr effect in a parity-time symmetric optomechanical system.

The cross-Kerr effects between the cavity and the mechanical oscillator in a parity-time symmetric optomechanical system are investigated. It is found that in the double-passive case there appears an asymmetric optomechanically induced transparency (OMIT) spectrum which is composed of a broad absorption peak located around the resonant point and a absorption line at the frequency position mainly determined by the Kerr interaction. The distinctive asymmetry induced by the cross-Kerr coupling is precisely demonstrated by the analytic findings. In the passive-active case, the resonance peaks in the OMIT spectrum are increased with the weak tunnel coupling, which is contrary to that in the double-passive case. When the tunnel coupling is increased up in the strong coupling region, the broad absorption peak and the absorption line in the OMIT spectrum are sequentially changed into the amplification ones, and the central amplification dip is split into two parts due to the normal mode splitting induced by the strong tunnel coupling. This can be used to realize a switching from absorption to amplification by only adjusting the tunnel interaction.

Triple tailored nonlinear dispersion of dressed four- and six-wave mixing

We investigate the spectral signals and spatial images of a probe transmission signal, four-wave mixing (FWM), and six-wave mixing (SWM) under double dressing effects in an inverted Y-type system. Especially, we get the triple tailored nonlinear dispersion (about 60 MHz) of the dressed FWM and SWM through the interaction between electromagnetically induced transparency (EIT) windows and the Kerr nonlinearity. Moreover, SWM and dressed FWM with narrow linewidth are obtained through the tailoring of the three EIT windows, which is much narrower than the EIT. In addition, we first elaborate the modulation effect from the self-Kerr coefficient of FWM on the spot. We also investigate the spatial characteristics (defocusing, shifting, and splitting) of FWM and SWM induced by tailored self-Kerr and cross-Kerr effects among the relative fields. Such spatial shifting, splitting induced by the tailored nonlinear dispersion can be used for a higher contrast and high speed switch as well as a high resolution router.

Entanglement concentration and purification of two-mode squeezed microwave photons in circuit QED

We present a theoretical proposal for a physical implementation of entanglement concentration and purification protocols for two-mode squeezed microwave photons in circuit quantum electrodynamics (QED). First, we give the description of the cross-Kerr effect induced between two resonators in circuit QED. Then we use the cross-Kerr media to design the effective quantum nondemolition (QND) measurement on microwave-photon number. By using the QND measurement, the parties in quantum communication can accomplish the entanglement concentration and purification of nonlocal two-mode squeezed microwave photons. We discuss the feasibility of our schemes by giving the detailed parameters which can be realized with current experimental technology. Our work can improve some practical applications in continuous-variable microwave-based quantum information processing.

Designing Kerr interactions using multiple superconducting qubit types in a single circuit

The engineering of Kerr interactions is of great interest for processing quantum information in multipartite quantum systems and for investigating many-body physics in a complex cavity-qubit network. We study how coupling multiple different types of superconducting qubits to the same cavity modes can be used to modify the self- and cross-Kerr effects acting on the cavities and demonstrate that this type of architecture could be of significant benefit for quantum technologies. Using both analytical perturbation theory results and numerical simulations, we first show that coupling two superconducting qubits with opposite anharmonicities to a single cavity enables the effective self-Kerr interaction to be diminished, while retaining the number splitting effect that enables control and measurement of the cavity field. We demonstrate that this reduction of the self-Kerr effect can maintain the fidelity of coherent states and generalised Schrödinger cat states for much longer than typical coherence times in realistic devices. Next, we find that the cross-Kerr interaction between two cavities can be modified by coupling them both to the same pair of qubit devices. When one of the qubits is tunable in frequency, the strength of entangling interactions between the cavities can be varied on demand, forming the basis for logic operations on the two modes. Finally, we discuss the feasibility of producing an array of cavities and qubits where intermediary and on-site qubits can tune the strength of self- and cross-Kerr interactions across the whole system. This architecture could provide a way to engineer interesting many-body Hamiltonians and be a useful platform for quantum simulation in circuit quantum electrodynamics.