cross-Kerr Interactions Research Articles

Improving the Stationary Entanglement of a Laguerre-Gaussian Cavity Mode with a Rotating Mirror via Nonlinear Cross-Kerr Interactions and Parametric Interactions.

Quantum entanglement is essential in performing many quantum information tasks. Here, we theoretically investigate the stationary entanglement between a Laguerre-Gaussian (LG) cavity field and a rotating end mirror in an LG-cavity optorotational system with a nonlinear cross-Kerr (CK) interaction and a degenerate optical parametric amplifier (OPA). We calculate the logarithmic negativity of the system to quantify the stationary entanglement. We examine the influence of various system parameters such as the cavity detuning, the strength of the nonlinear CK interaction, the parametric gain and phase of the OPA, the power of the input Gaussian laser, the topological charge of the LG-cavity field, the mass of the rotating end mirror, and the ambient temperature on the stationary entanglement. Under the combined effect of the nonlinear CK interaction and the OPA, we find that the stationary entanglement can be substantially enhanced at lower Gaussian laser powers, smaller topological charges of the LG-cavity field, and larger masses of the rotating end mirror. We show that the combination of the nonlinear CK interaction and the OPA can make the stationary entanglement more robust against the ambient temperature.

Electrically coupled optomechanical cavities as a tool for quantum nondemolition measurement

We present a new model of two electrically coupled optomechanical cavities. This model is based on the recently presented proposal [Physical Review A 103 (2021) 043509]. We found that coupling two optomechanical cavities via Coulomb force leads to cross-Kerr interactions between those cavities. We show that such systems may be ideal for a protocol of quantum non-demolition measurement because it is easy to eliminate the self-phase modulation effect. Moreover, nonlinearities in our model are based on easily adjustable parameters, and therefore, given recent experimental studies, we believe that experimental realization of a cross-Kerr interaction via Coulomb force coupling is feasible.

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.

A two-photon laser in a Kerr-like medium with cross-Kerr and intensity-dependent coupling

We have studied the photon statistics of a nondegenerate two-photon laser with a medium that has both self- and cross-Kerr interactions as well as intensity-dependent atom–field coupling in the Hamiltonian. The density matrix equation of the atoms and two-mode cavity fields was derived using the standard Scully–Lamb approach and numerically solved. Under certain conditions, the photon distribution function equation was derived and solved analytically. The first few moments of photon numbers were calculated in the region above the lasing threshold. Nonclassicality of the fields was investigated by means of the Mandel Q parameter, second-order correlation functions and the Cauchy–Schwarz inequality. The results are analyzed for a range of finite Kerr parameters. Intensity-dependent coupling suppresses the nonclassicality of the field. It pushes the statistics of the field towards super-Poissonian.The self- and cross-Kerr interactions have significant roles in the nonclassicality of the two-photon cavity field and its statistics. These results are interesting for the field of quantum nonlinear optics and useful in quantum communications.

Time evolution of two harmonic oscillators with cross-Kerr interactions

We study the time evolution of two coupled quantum harmonic oscillators interacting through nonlinear optomechanical-like Hamiltonians that include cross-Kerr interactions. We employ techniques developed to decouple the time-evolution operator and obtain the analytical solution for the time evolution of the system. We apply these results to obtain explicit expressions of a few quantities of interest. Our results do not require approximations and therefore allow us to study the nature and implications of the full nonlinearity of the system. As a potential application, we show that it is possible to greatly increase the population of phonons using a suitable combination of cubic and cross-Kerr interactions.

Machine learning method for state preparation and gate synthesis on photonic quantum computers

We show how techniques from machine learning and optimization can be used to find circuits of photonic quantum computers that perform a desired transformation between input and output states. In the simplest case of a single input state, our method discovers circuits for preparing a desired quantum state. In the more general case of several input and output relations, our method obtains circuits that reproduce the action of a target unitary transformation. We use a continuous-variable quantum neural network as the circuit architecture. The network is composed of several layers of optical gates with variable parameters that are optimized by applying automatic differentiation using the TensorFlow backend of the Strawberry Fields photonic quantum computer simulator. We demonstrate the power and versatility of our methods by learning how to use short-depth circuits to synthesize single photons, Gottesman–Kitaev–Preskill states, NOON states, cubic phase gates, random unitaries, cross-Kerr interactions, as well as several other states and gates. We routinely obtain high fidelities above 99% using short-depth circuits, typically consisting of a few hundred gates. The circuits are obtained automatically by simply specifying the target state or gate and running the optimization algorithm.

Tuneable hopping and nonlinear cross-Kerr interactions in a high-coherence superconducting circuit

Analog quantum simulations offer rich opportunities for exploring complex quantum systems and phenomena through the use of specially engineered, well-controlled quantum systems. A critical element, increasing the scope and flexibility of such experimental platforms, is the ability to access and tune in situ different interaction regimes. Here, we present a superconducting circuit building block of two highly coherent transmons featuring in situ tuneable photon hopping and nonlinear cross-Kerr couplings. The interactions are mediated via a nonlinear coupler, consisting of a large capacitor in parallel with a tuneable superconducting quantum interference device (SQUID). We demonstrate the working principle by experimentally characterising the system in the single-excitation and two-excitation manifolds, and derive a full theoretical model that accurately describes our measurements. Both qubits have high coherence properties, with typical relaxation times in the range of 15 to 40 μs at all bias points of the coupler. Our device could be used as a scalable building block in analog quantum simulators of extended Bose-Hubbard and Heisenberg XXZ models, and may also have applications in quantum computing such as realising fast two-qubit gates and perfect state transfer protocols.

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.

Quantum Feedback Control for Deterministic Entangled Photon Generation

We present quantum feedback control for deterministic entanglement generation at the single-photon level. The protocol of controlling both total photon number and phase difference is based on the cascade structure of cavities placed in an optical closed loop, quantum nondemolition measurement with cross-Kerr interactions, and Lyapunov stability for feedback design.