Nonlinear optical media of Kerr type are described by a particular version of an anharmonic quantum harmonic oscillator. The dynamics of this system can be described using the Moyal equations of motion, which correspond to a quantum phase space representation of the Heisenberg equations of motion. For the Kerr system we derive exact solutions of the Moyal equations for a complete set of observables formed from the photon creation and annihilation operators. These Moyal solutions incorporate the asymptotics of the classical limit in a simple explicit form. An unusual feature of these solutions is that they exhibit periodic singularities in the time variable. These singularities are removed by the phase space averaging required to construct the expectation value for an arbitrary initial state. Nevertheless, for strongly number-squeezed initial states the effects of the singularity remain observable.
States of nonlinear quantum oscillators (f-oscillators) are considered in the Weyl-Wigner-Moyal representation and the tomographic probability representation, where the states are described by standard probability distributions instead of wave functions or density matrices. The evolving integrals of motion for classical and quantum f-oscillators are found and the solution for the Liouville equation associated with the probability distribution on the phase space for this oscillator is obtained along with the solution of Moyal equation for quantum f-oscillator, which provide the solutions for pa…
We apply the Green's function method to determine the global degree of squeezing and the transverse spatial distribution of quantum fluctuations of solitons in Kerr media. We show that both scalar bright solitons and multimode vector solitons experience strong squeezing on the optimal quadrature. For vector solitons, this squeezing is shown to result from an almost perfect anti-correlation between the fluctuations on the two incoherently-coupled circular polarisations.
A quantum theory of 3D X-shaped optical bullets in Kerr media is presented. The existence of progressive undistorted squeezed vacuum is predicted. Applications to quantum non-demolition experiments, entanglement and interferometers for gravitational waves detection are envisaged.
A scalar Wigner distribution function for describing polarized light is proposed in analogy with the treatment of spin variables in quantum kinetic theory. The formalism is applied to the propagation of circularly polarized light in nonlinear Kerr media and an extended phase space evolution equation is derived along with invariant quantities. We further consider modulation instability as well as the extension to partially coherent fields.
Two nonlinear Kerr oscillators mutually coupled by parametric pumping are studied as a source of states entangled in photon numbers. Temporal evolution of entanglement quantified by negativity shows the effects of sudden death and birth of entanglement. Entanglement is preserved even in asymptotic states under certain conditions. The role of reservoirs at finite temperature in entanglement evolution is elucidated. Relation between generation of entangled states and violation of Cauchy-Schwartz inequality for oscillator intensities is found.
We present a scheme for the quantum teleportation of the polarization state of a photon employing a cross-Kerr medium. The experimental feasibility of the scheme is discussed and we show that, using the recently demonstrated ultraslow light propagation in cold atomic media, our proposal can be realized with presently available technology.
Phase shifts induced by the Kerr effect are usually very small at the single-photon level. We propose two circuits for enhancing the cross-Kerr phase shift by applying one- and two-mode quadrature squeezing operators. Our results are based on the vector coherent state theory and can be implemented by physical operations satisfying the commutation relations for generators of the generalized special unitary group SU(1,1). While the proposed methods could be useful for the realization of quantum optical entangling gates based on Kerr nonlinear media at the single-photon level, they also indicate …
We present a method for implementing a weak optical Kerr interaction (single-mode Kerr Hamiltonian) in a measurement-based fashion using the common set of universal elementary interactions for continuous-variable quantum computation. Our scheme is a conceptually distinct alternative to the use of naturally occurring, weak Kerr nonlinearities or specially designed nonlinear media. Instead, we propose to exploit suitable offline prepared quartic ancilla states together with beam splitters, squeezers, and homodyne detectors. For perfect ancilla states and ideal operations, our decompositions for …
Quantum nonlinear operations for harmonic oscillator systems play a key role in the development of analog quantum simulators and computers. Since a variety of strong highly nonlinear operations are unavailable in the existing physical systems, it is a common practice to approximate them by using conditional measurement-induced methods. The conditional approach has several drawbacks, the most severe of which is the exponentially decreasing success rate of the strong and complex nonlinear operations. We show that by using a suitable two level system sequentially interacting with the oscillator, …
We investigate the spatio-temporal evolution of a Gaussian probe pulse propagating through a four-level $N$-type atomic medium. At two-photon resonance of probe-and control fields, weaker probe pulses may propagate through the medium with low absorption and pulse shape distortion. In contrast, we find that increasing the probe pulse intensity leads to a splitting of the initially Gaussian pulse into a sequence of subpulses in the time domain. The number of subpulses arising throughout the propagation can be controlled via a suitable choice of the probe and control field parameters. Employing a…
Amplifier is at the heart of almost all experiment carrying out the precise measurement of a weak signal. An idea amplifier should have large gain and minimum added noise simultaneously. Here, we consider the quantum measurement properties of a hybrid nonlinear cavity with the Kerr and OPA nonlinear media to amplify an input signal. We show that our hybrid-nonlinear-cavity amplifier has large gain in the single-value stable regime and achieves quantum limit unconditionally.
Strong long-range coupling between distant spins is crucial for spin-based quantum information processing. However, achieving such a strong spin-spin coupling remains challenging. Here we propose to realize a strong coupling between two distant spins via the Kerr effect of magnons in a yttrium-iron-garnet nanosphere. By applying a microwave field on this nanosphere, the Kerr effect of magnons can induce the magnon squeezing, so that the coupling between the spin and the squeezed magnons can be exponentially enhanced. This in turn allows the spin-magnon distance to increase from nano- to microm…
We present a unified theoretical study of the bright solitons governed by self-focusing and defocusing nonlinear Schrodinger (NLS) equations with generalized parity-time (PT)-symmetric Scarff II potentials. Particularly, a PT-symmetric k-wavenumber Scarff II potential and a multi-well Scarff II potential are considered, respectively. For the k-wavenumber Scarff II potential, the parameter space can be divided into different regions, corresponding to unbroken and broken PT-symmetry and the bright solitons for self-focusing and defocusing Kerr nonlinearities. For the multi-well Scarff II potenti…
We present a complete and consistent quantum theory of generalised X waves with orbital angular momentum (OAM) in dispersive media. We show that the resulting quantised light pulses are affected by neither dispersion nor diffraction and are therefore resilient against external perturbations. The nonlinear interaction of quantised X waves in quadratic and Kerr nonlinear media is also presented and studied in detail.
We give explicit criteria for the reflectionlessness, transparency, and invisibility of a finite-range potential in the presence of an incoherent (intensity-dependent) nonlinearity that is confined to the range of the potential. This allows us to conduct a systematic study of the effects of such a nonlinearity on a locally periodic class of finite-range potentials that display perturbative unidirectional invisibility. We use our general results to examine the effects of a weak Kerr nonlinearity on the behavior of these potentials and show that the presence of nonlinearity destroys the unidirec…
We present here an all--optical scheme for the experimental realization of a quantum phase gate. It is based on the polarization degree of freedom of two travelling single photon wave-packets and exploits giant Kerr nonlinearities that can be attained in coherently driven ultracold atomic media.
Quantum Dispersive Waves and Multimode Squeezing in Pure-Kerr Parametrically Driven Cavity Solitons
Institute for Physical Science and Technology, University of Maryland（马里兰大学物理科学与技术研究所）；Department of Physics, University of Maryland（马里兰大学物理系）；Department of Mechanical Engineering, University of Maryland（马里兰大学机械工程系）；University of Maryland Baltimore County（马里兰大学巴尔的摩县分校）；National Quantum Laboratory (QLab) at Maryland（马里兰国家量子实验室）
Any optical quantum information processing machine would be comprised of fully-characterized constituent devices for both single state manipulations and tasks involving the interaction between multiple quantum optical states. Ideally for the latter, would be an apparatus capable of deterministic optical phase shifts that operate on input quantum states with the action mediated solely by auxiliary signal fields. Here we present the complete experimental characterization of a system designed for optically controlled phase shifts acting on single-photon level probe coherent states. Our setup is b…
We study a new class of vector solitons in trapped Nonlinear Schrodinger systems modelling the dynamics of coupled light beams in GRIN Kerr media and atomic mixtures in Bose-Einstein condensates. These solitons exist for different spatial dimensions, their existence is studied by means of a systematic mathematical technique and the analysis is made for inhomogeneous media.
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 p…
We present a realization of two-qubit controlled-phase gate, based on the linear and nonlinear properties of the probe and signal optical pulses in an asymmetric GaAs/AlGaAs double quantum wells. It is shown that, in the presence of cross-phase modulation, a giant cross-Kerr nonlinearity and mutually matched group velocities of the probe and signal optical pulses can be achieved while realizing the suppression of linear and self-Kerr optical absorption synchronously. These characteristics serve to exhibit an all-optical two-qubit controlled-phase gate within efficiently controllable photon-pho…
Photons are ideal carriers for quantum information as they can have a long coherence time and can be transmitted over long distances. These properties are a consequence of their weak interactions within a nearly linear medium. To create and manipulate nonclassical states of light, however, one requires a strong, nonlinear interaction at the single photon level. One approach to generate suitable interactions is to couple photons to atoms, as in the strong coupling regime of cavity QED systems. In these systems, however, one only indirectly controls the quantum state of the light by manipulating…
The existence and stability of the nonlinear spatial localized modes are investigated in parity-time symmetric optical media characterized by a generic complex hyperbolic refractive index distribution with competing gain and loss profile. The exact analytical expressions of the localized modes are found for all values of the competing parameter and in the presence of both the self-focusing and self-defocusing Kerr nonlinearity. The effect of competing gain/loss profile on the stability structure of these localized modes are discussed with the help of linear stability analysis followed by the d…
Light in a dielectric medium moves slower than in vacuum. The corresponding electromagnetic field equations are then no longer invariant under ordinary Lorentz transformations, but only under such transformations corresponding to this reduced velocity. Based on this physical symmetry, an effective theory for low-energy electromagnetic phenomena in dielectrics is constructed. It has none of the problems of the old formulations of Minkowski and Abraham. Dispersion in the optical regime and the Kerr effect arise in a natural way from higher order interaction terms. The effective field theory is q…
