C. Sudheesh, S. Lakshmibala, V. Balakrishnan
We investigate non-classical effects such as fractional revivals, squeezing and higher-order squeezing of photon-added coherent states propagating through a Kerr-like medium.The Wigner functions corresponding to these states at the instants of fractional revivals are obtained, and the extent of non-classicality quantified.
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We have investigated the cross Kerr phase shift of propagating microwave fields strongly coupled to an artificial atom. The artificial atom is a superconducting transmon qubit in an open transmission line. We demonstrate average phase shifts of 11 degrees per photon between two coherent microwave fields both at the single-photon level. At high control power, we observe phase shifts up to 30 degrees. Our results provide an important step towards quantum gates with propagating photons in the microwave regime.
A cross-Kerr interaction produces a phase shift on two modes of light proportional to the number of photons in both modes, and is sometimes called cross-phase modulation. Cross-Kerr nonlinearities have many applications in classical and quantum nonlinear optics, including the possibility of a deterministic and all-optical controlled-phase gate. We calculate the one- and two-photon S-matrix for fields propagating in a medium where the cross-Kerr interaction is spatially distributed at discrete interaction sites comprised of atoms. For the interactions considered, we analyze the cases where the …
We theoretically study the optical tomography of the time evolved states generated by the evolution of different kinds of initial wave packets in a Kerr medium. Exact analytical expression for the optical tomogram of the quantum state at any instant during the evolution of a generic initial wave packet is derived in terms of Hermite polynomials. Time evolution of the optical tomogram is discussed for three kinds of initial states: a coherent state, an $m$-photon-added coherent state, and even and odd coherent states. We show the manifestation of revival and fractional revivals in the optical t…
We show in the framework of a tractable model that revivals and fractional revivals of wave packets afford clear signatures of the extent of departure from coherence and from Poisson statistics of the matter wave field in a Bose-Einstein condensate, or of a suitably chosen initial state of the radiation field propagating in a Kerr-like medium.
We analyze both analytically and numerically the resonant four-wave mixing of two co-propagating single-photon wave packets. We present analytic expressions for the two-photon wave function and show that soliton-type quantum solutions exist which display a shape-preserving oscillatory exchange of excitations between the modes. Potential applications including quantum information processing are discussed.
Exact propagating Dirac wave packets in an attractive Coulomb-like potential
在轴对称势V=-v0/ρ中构造了狄拉克方程的正能量可归一化波包精确解，发现概率密度与自旋取向解耦，并在临界耦合时时间演化完全冻结。
Treating the ideal coherent state as a reference state, the effects due to departure from coherence of an initial wave packet propagating through a nonlinear medium, were examined, specifically in the context of non-classical effects such as revivals, fractional revivals, squeezing and higher-order squeezing during its temporal evolution. Further, these studies were extended to examine the role of quantum entanglement in bipartite systems. The dynamics of quantum expectation values were tracked carefully in various cases and the conditions under which a wave packet spreads chaotically, were in…
Wave packet revivals and fractional revivals are striking quantum interference phenomena that can occur under suitable conditions in a system with a nonlinear spectrum. In the framework of a specific model (the propagation of an initially coherent wave packet in a Kerr-like medium), it is shown that distinctive signatures of these revivals and fractional revivals are displayed by the time evolution of the expectation values of physical observables and their powers, i.e., by experimentally measurable quantities. Moreover, different fractional revivals can be selectively identified by examining …
An analytical treatment of a propagating wave packet incident on a transient barrier reveals a counterintuitive quantum mechanical effect in which, for a particular time interval, the time-varying transmission probability {\it exceeds} (`superarrival') that for the free propagation of the wave packet. It is found that the speed with which the information about the barrier perturbation propagates across the wave packet can exceed the group velocity of the wave packet. An interesting implication of this effect regarding information transfer is analyzed by showing one-to-one correspondence betwee…
We derive quantum trajectories (also known as stochastic master equations) that describe an arbitrary quantum system probed by a propagating wave packet of light prepared in a continuous-mode Fock state. We consider three detection schemes of the output light: photon counting, homodyne detection, and heterodyne detection. We generalize to input field states that are superpositions and or mixtures of Fock states and illustrate the formalism with several examples.
We study the dynamics of superposed wave packets in a specific nonlinear Hamiltonian which models the wave packet propagation in Kerr-like media and the dynamics of Bose-Einstein condensates. We show the dependence of initial wave packet superposition on fractional revival times using analysis based on the expectation values, Rényi entropy and Wigner function. We also show how the selective identification of fractional revivals using moments of appropriate observables depends on the number of wave packets present in the initial state.
We present a Maxwell-Bloch description of the dynamics of a light pulse propagating through a spatially inhomogeneous system consisting of alternating layers of EIT media and vacuum. We study the effect of a dynamical modulation of the EIT control field on the shape of the wave packet: interesting effects due to the presence of interfaces with group velocity mismatch are found. An effective description based on a continuity equation is developed. Modulation schemes that can be realized in ultracold atomic samples with standard experimental techniques are proposed and discussed.
We report an experimental study of group-velocity dispersion effect on an entangled two-photon wavepacket, generated via spontaneous parametric down-conversion and propagating through a dispersive medium. Even in the case of using CW laser beam for pump, the biphoton wavepacket and the second-order correlation function spread significantly. The study and understanding of this phenomenon is of great importance for quantum information applications, such as quantum communication and distant clock synchronization.
We identify and discuss nonlinear phase noise arising in Kerr self-phase modulation of a coherent light pulse propagating through an attenuating medium with third-order nonlinearity in a dispersion-free setting. This phenomenon, accompanying the standard unitary Kerr transformation of the optical field, is described with high accuracy as Gaussian phase diffusion with parameters given by closed expressions in terms of the system properties. We show that the irreversibility of the nonlinear phase noise ultimately limits the ability to transmit classical information in the phase variable over a l…
The self-Kerr interaction is an optical nonlinearity that produces a phase shift proportional to the square of the number of photons in the field. At present, many proposals use nonlinearities to generate photon-photon interactions. For propagating fields these interactions result in undesirable features such as spectral correlation between the photons. Here, we engineer a discrete network composed of cross-Kerr interaction regions to simulate a self-Kerr medium. The medium has effective long-range interactions implemented in a physically local way. We compute the one- and two-photon S matrice…
Unbound wave packets propagating to macroscopic space and time coordinates become proportional to their (Fourier transform) momentum distribution at earlier times whereby the asymptotic coordinates and the initial momenta are connected everywhere by appropriate classical trajectories. This asymptotic imaging theorem is relevant to every quantum reaction involving macroscopic extraction and detection of fragments emerging from a microscopic volume. It justifies the usual assumption of classical particle motion used in the design of particle detectors. We illustrate this quantum to semiclassical…
Closed-form, normalizable solutions of Dirac's equation propagating within a semi-infinite cylindrical waveguide are obtained in terms of ordinary and modified Bessel functions. These relativistic wave packets induce quantum backflow on a cross-section of the cylinder at practically any distance along the waveguide, becoming spin-polarized in the nonrelativistic limit. The predicted backflow is stable in time and is manifest regardless of the initial wave function.
In the paper, we employ a wavefunction approach to investigate the evolution of a two-photon wave packet propagating in a one-dimensional waveguide coupled to the Jaynes-Cummings (JC) system. We derive and solve, both analytically and numerically, a set of equations of motion governing the quantum state of the system. That allows us to provide real-time analysis of the evolution of the wave packet two-photon joint spectrum (2PJS) and the excitation dynamics of the JC system in the course of its interaction with the two-photon pulse. We demonstrate that the 2PJS and the spectrum of the wave pac…
The dynamic Stark shift results from the interaction of an atom with the electromagnetic field. We show how a propagating single-photon wave packet can induce a time-dependent dynamical Stark shift on a two-level system (TLS). A non-perturbative fully-quantum treatment is employed, where the quantum dynamics of both the field and the TLS are analyzed. We also provide the means to experimentally access such time-dependent frequency by measuring the interference pattern in the electromagnetic field inside a one-dimensional (1D) waveguide. The effect we evidence here may find applications in the …
Subtraction and Addition of Propagating Photons by Two-Level Emitters
本文提出利用被动二能级发射体的集体光-物质相互作用，在传播光场中高效实现单光子减除与逐个添加，从而以超过96.7%的总成功概率构建任意大Fock态，显著优于线性光学预告方案。
Wave packet dynamics of entangled q-deformed states
本研究针对Kerr型非线性介质中q形变场与原子作用的系统，探究两类初始q形变态的纠缠波包动力学，发现q形变会消除波包回复现象，大q值下呈混沌特性，还找到分束器作用下实现最大纠缠的最优q参数。
We study phase contributions of wave functions that occur in the evolution of Gaussian surface gravity water wave packets with nonzero initial momenta propagating in the presence and absence of an effective external linear potential. Our approach takes advantage of the fact that in contrast to matter waves, water waves allow us to measure both their amplitudes and phases.
Controllable single-photon wave packet scattering in two-dimensional resonator array by a giant atom
本研究针对二维光子谐振器阵列与巨型原子的非局域耦合体系，通过迭代制备稳定入射波包，调节耦合强度实现单光子波包的可控对称/非对称散射，发现散射中原子激发概率可忽略，为二维体系中按需生成光子态提供新方法。
Wave packet description of Majorana neutrino oscillations in a magnetic field
研究了Majorana中微子在磁场中的振荡行为，推导了考虑退相干效应的振荡概率表达式，并分析了相干长度与频率关系。
Fractional Revival Dynamics in Kerr-Type Systems: Angular Momentum Moments and Classical Analogs
本文研究Kerr型系统中角动量矩的分数复活动力学及经典类比，揭示量子与经典系统中复活现象的共性。
Chiral photon blockade in the spinning Kerr resonator
提出通过旋转非线性光学谐振腔实现手性光子阻塞，利用旋转诱导的时间反演对称性破缺使反向传播模式产生不同量子效应，并实现抵御背向散射损耗的稳健非经典关联，将光学手性对称性研究扩展至纯量子领域。
Particle delocalization is a common feature of quantum random walks in arbitrary lattices. However, in the typical scenario a particle spreads over multiple sites and its evolution is not directly useful for controlled quantum interferometry, as may be required for technological applications. In this paper we devise a strategy to perfectly split the wave-packet of an incoming particle into two components, each propagating in opposite directions, which reconstruct the shape of the initial wavefunction after a particular time $t^*$. Therefore, a particle in a delta-like initial state becomes exa…
Wave Packet Sizes in Quantum Mechanical Scatterings: New Perspective
本文针对量子力学散射中依赖环境与实验条件的波包尺寸，结合束缚态与传播波包的尺寸决定因素，开展系统分析，为相关研究提供新视角。
Quantum Control of an Oscillator with a Kerr-cat Qubit
本研究实验实现Kerr-cat量子比特与高品质因子微波腔的受驱参量耦合，演示腔的通用量子控制门集，通过频率选择性耗散抵消加热消除额外相位阻尼，为用Kerr-cat容错测量玻色编码误差症状奠定基础。
With propagating through a dispersive medium, the temporal-spectral profile of laser pulses should be inevitably modified. Although such dispersion effect has been well studied in classical optics, its effect on a single-photon wave-packet, i.e., the matter wave of a single-photon, has not yet been entirely revealed. In this paper, we investigate the effect of dispersion on indistinguishability of single-photon wave-packets through the Hong-Ou-Mandel (HOM) interference. By dispersively manipulating two indistinguishable single-photon wave-packets before interfering with each other, we observe …
The cross-Kerr effect is studied for two pulses propagating in an atomic medium in a tripod configuration, dressed by a strong standing wave coupling beam. Nonlinear phase shifts for both transmitted and reflected beams are calculated taking into account the redistribution of the population among the atomic levels which allows one to study the phase shifts in a wide range of pulse detunings. The influence of other parameters, e.g., the intensity of the control field and the relaxation rates, on the cross-Kerr effect is also examined in detail.
We discuss the feasibility of a quantum nondemolition measurement (QND) of photon number based on cross phase modulation due to the Kerr effect in Photonic Crystal Waveguides (PCWs). In particular, we derive the equations for two modes propagating in PCWs and their coupling by a third order nonlinearity. The reduced group velocity and small cross-sectional area of the PCW lead to an enhancement of the interaction relative to bulk materials. We show that in principle, such experiments may be feasible with current photonic technologies, although they are limited by material properties. Our analy…
Ballistic transport through nanoscale devices with time-dependent Rashba-type spin-orbit interaction (SOI) can lead to spin-polarized wave packets that appear even for completely unpolarized input. The SOI that oscillates in a finite domain generates density and spin polarization fluctuations that leave the region as propagating waves. Particularly, spin polarization has space and time dependence even in regions without SOI. Our results are based on an analytic solution of the time-dependent Schrödinger equation. The relevant Floquet quasi-energies that are obtained appear in the energy spectr…
A surprising feature of the Kerr metric is the anisotropy of the speed of light. The angular momentum of a rotating massive object causes co- and counter-propagating light paths to move at faster and slower velocities, respectively as determined by a far-away clock. Based on this effect we derive ultimate quantum limits for the measurement of the Kerr rotation parameter $a$ using a interferometric set up. As a possible implementation, we propose a Mach-Zehnder interferometer to measure the "one-way height differential" time effect. We isolate the effect by calibrating to a dark port and rotati…
We propose and develop a concept of magnonic logic gates enabling reversible computing. The gates consist of passive elements: waveguides, cross-junctions and phase shifters. Logical 0 and 1 are encoded in the relative phase of the propagating spin wave packets (0 or π). The gates contain several possible trajectories for each packet to propagate from the input to the output. Re-direction of the spin wave packets among the possible trajectories is due to the interference in the magnetic cross-junctions. Two wave packets coming to the cross-junction in-phase propagate through the junction witho…
Non-Linear Interference Challenging Topological Protection of Chiral Edge States
本研究发现Floquet拓扑系统中的非线性散射效应可挑战手性边缘态的拓扑保护，波包碰撞结果可由相对相位调控，并提出耦合波导和冷原子凝聚体两个实验验证平台。
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…
We propose a single optical photon source for quantum cryptography based on the acousto-electric effect. Surface acoustic waves (SAWs) propagating through a quasi-one-dimensional channel have been shown to produce packets of electrons which reside in the SAW minima and travel at the velocity of sound. In our scheme these electron packets are injected into a p-type region, resulting in photon emission. Since the number of electrons in each packet can be controlled down to a single electron, a stream of single (or N) photon states, with a creation time strongly correlated with the driving acoust…
We propose a deterministic, measurement-free implementation of a cubic phase gate for continuous-variable quantum information processing. In our scheme, the applications of displacement and squeezing operations allow us to engineer the effective evolution of the quantum state propagating through an optical Kerr nonlinearity. Under appropriate conditions, we show that the input state evolves according to a cubic phase Hamiltonian, and we find that the cubic phase gate error decreases inverse-quartically with the amount of quadrature squeezing, even in the presence of linear loss. We also show h…
The competition between staggered imaginary potentials and lattice dimerization results in a unidirectional propagating coalescing state of a non-Hermitian Su-Schrieffer-Heeger (SSH) ring at an exceptional point. A segment of the SSH ring inherits the unidirectional feature and exhibits some intriguing dynamic behaviors when it is embedded in a Hermitian chain as a $\mathcal{PT}$-symmetric scattering center. Based on the Bethe ansatz scattering solution for the interface between Hermitian and non-Hermitian regions, we show that the SSH scattering center supports the following wave-packet dynam…
The influence of quantum fluctuations of the electromagnetic field on the propagation of a polarized light wave in a nonlinear dielectric is investigated. It is shown that in some cases, the fluctuations couple to the optical nonlinearities of the medium and make its refractive index dependent on the polarization of the propagating wave. As a consequence, two light waves propagating in a same direction but with different polarizations will have different speeds, so there will be a Kerr-effect birefringence induced by quantum fluctuations. We consider the case of the electromagnetic field in a …
Ultrahigh free-electron Kerr nonlinearity in all-semiconductor waveguides for all-optical nonlinear modulation of mid-infrared light
本研究通过全半导体波导实现超高水平自由电子 Kerr 非线性，用于中红外光的高效非线性调制，为光子集成电路发展提供新途径。
Doppler-induced tunable and shape-preserving frequency conversion of microwave wave packets
本文提出了一种利用动态多普勒效应实现微波波包频率转换的方法，实现了高达3.7%的频率偏移同时保持波包时间形状，具有可调性和任意频率模式印制能力。
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