Magdalena Stobińska, G. J. Milburn, Krzysztof Wódkiewicz
We present an effective method of coherent state superposition (cat state) generation using single trapped ion in a Paul trap. The method is experimentally feasible for coherent states with amplitude $α\le 2$ using available technology. It works both in and beyond the Lamb-Dicke regime.
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Generation of Large Kitten states via thermally driven dissipative freezing
本研究利用磁量子数为0的Dicke态正交基表示与耗散单轴扭转，提高大Kitten态乃至Cat态的产生概率，并以光发射率预示成功。
We report preparation and characterization of coherent superposition states t |0> + alpha |1> of electromagnetic field by conditional measurements on a beamsplitter. The state is generated in one of the beam splitter output channels if a coherent state and a single-photon Fock state |1> are present in the two input ports and a single photon is registered in the other beam splitter output. The single photon thus plays a role of a "catalyst": it is explicitly present in both the input and the output channels of the interaction yet facilitates generation of a nonclassical state of light.
Breeding the Cat Through Superposition of Two Schrodinger Kittens Based on Coupled Waveguides
针对高振幅光学薛定谔猫态难以制备的问题，提出在耦合波导中叠加两个小猫态并使其干涉增长的方案，实现高概率、可片上集成的大振幅猫态生成。
A quantitative analysis is conducted on the impacts of experimental imperfections in the input state, the detector properties, and their interactions on photon-subtracted squeezed vacuum states in terms of a quantum non-Gaussian character witness and Wigner function. Limitations of the non-classicality and quantum non-Gaussian characteristic of Schrödinger kitten states are identified and addressed. The detrimental effects of a photon-number detector on the generation of odd Schrödinger kitten state at near-infrared wavelengths ($\sim$ 860 nm) and telecommunication wavelengths ($\sim$ 1550 nm)…
We study the nonclassicality of the evolution of a superposition of an arbitrary number of photon-added squeezed coherent Schrödinger cat states in a nonlinear Kerr medium. The nonlinearity of the medium gives rise to the periodicities of the quantities such as the Wehrl entropy $S_{Q}$ and the negativity $δ_{W}$ of the $W$-distribution, and a series of local minima of these quantities arise at the rational submultiples of the said period. At these local minima the evolving state coincides with the transient Yurke-Stoler type of photon-added squeezed kitten states, which, for the choice of the…
The Wehrl information entropy and its phase density, the so-called Wehrl phase distribution, are applied to describe Schrödinger cat and cat-like (kitten) states. The advantages of the Wehrl phase distribution over the Wehrl entropy in a description of the superposition principle are presented. The entropic measures are compared with a conventional phase distribution from the Husimi Q-function. Compact-form formulae for the entropic measures are found for superpositions of well-separated states. Examples of Schrödinger cats (including even, odd and Yurke-Stoler coherent states), as well as the…
Tailoring optical Schrödinger cat states via orientation-dependent high-harmonic generation in $\rm{H}_2^+$
研究通过H₂⁺中与取向相关的高次谐波产生定制光学薛定谔猫态，结合含时薛定谔方程模拟与HHG框架，在两种互补策略下评估维格纳函数，利用跃迁规则及干涉实现转变，且交叉与多种因素解耦，提供独特控制。
The cat state is shown to `store' a single photon through the superposition of its orthogonal counterpart with itself, and an excited oscillator state. Photon addition leads to a $π$ phase shift at origin in the observed phase space interference of the Wigner function, which also displays negativity, controlled by the average photon number ($|α|^2$) of coherent states comprising the cat state. The maxima and minima of the sub-Planck tiles in the phase space of the kitten state are interchanged after photon addition, leading to their orthogonality. Interestingly, photon addition to Yurke-Stoler…
Cat states are systems in a superposition of macroscopically distinguishable states; this superposition can be of either classically or quantum distinct state, regardless of the number of particles or modes involved. Here, we constructed an experimental model that simulates an optical cat state by engineering the classical orbital angular momentum of light, referred to here as an analogous cat state (a-CS). In our scheme, the behaviors of the a-CS in position space show many similarities to the quantum version of the optical cat state in phase space, for example, movement, rotation, and interf…
Recently, using conditioning approaches on the high-harmonic generation process induced by intense laser-atom interactions, we have developed a new method for the generation of optical Schrödinger cat states (M. Lewenstein et al., arXiv:2008.10221 (2020)). These quantum optical states have been proven to be very manageable as, by modifying the conditions under which harmonics are generated, one can interplay between $\textit{kitten}$ and $\textit{genuine cat}$ states. Here, we demonstrate that this method can also be used for the development of new schemes towards the creation of optical Schrö…
Recently, intensely driven laser-matter interactions have been used to connect the fields of strong laser field physics with quantum optics by generating non-classical states of light. Here, we make a further key step and show the potential of strong laser fields for generating controllable high-photon-number coherent-state superpositions. This has been achieved by using two of the most prominent strong-laser induced processes: high-harmonic generation and above-threshold ionization. We show how the obtained coherent-state superpositions change from an optical Schrödinger "cat" state to a "kit…
Cat states, which were initially proposed to manifest macroscopic superpositions, play an outstanding role in fundamental aspects of quantum dynamics. In addition, they have potential applications in quantum computation and quantum sensing. However, cat states are vulnerable to dissipation, which puts the focus of cat-state generation on higher speed and increased robustness. Dissipative cat-state generation is a common approach based on the nonlinear coupling between a lossy pump field and a half-frequency signal field. In such an approach, the pump field is usually kept in equilibrium, which…
The four-component cat state represents a particularly useful quantum state for realizing fault-tolerant continuous variable quantum computing. While such encoding has been experimentally generated and employed in the microwave regime, the states have not yet been produced in the optical regime. Here we propose a simple linear optical circuit combined with photon counters for the generation of such optical four-component cat states. This work might pave the way for the first experimental generation of fault-tolerant optical continuous variable quantum codes.
We present what is to our knowledge the first implementation of a Schrödinger cat states "breeding" operation, which allows an iterative growth of these states. We thus report the experimental generation of a squeezed Schrödinger cat state from two single photon Fock states, which can be seen as cat states with zero amplitude. These Fock states are mixed on a symmetrical beamsplitter and the generation is heralded by a homodyne measurement in one of the two output arms. The output state has a fidelity of 61% with an even squeezed Schrödinger cat state of amplitude $α=1.63$. This hybrid operati…
Programmable generation of flying cat-qubits
提出利用非线性玻色系统中的时间依赖双光子驱动直接从真空生成飞行猫量子比特，通过工程化Kerr非线性和耗散实现逻辑控制，并分析噪声下的鲁棒性。
Generation of multicomponent Schrödinger cat states in schemes with measurement of Gaussian states
本研究提出基于多模高斯态光子数分辨测量的方案，产生粒子数差4或8的福克态叠加态，经与多组分薛定谔猫态对比，评估保真度缩放规律并推导最优配置。
We propose a high-rate generation method of optical Schrödinger's cat states. Thus far, photon subtraction from squeezed vacuum states has been a standard method in cat-state generation, but its constraints on experimental parameters limit the generation rate. In this paper, we consider the state generation by photon number measurement in one mode of arbitrary two-mode Gaussian states, which is a generalization of conventional photon subtraction, and derive the conditions to generate high-fidelity and large-amplitude cat states. Our method relaxes the constraints on experimental parameters, al…
Spin cat states are promising candidates for achieving Heisenberg-limited quantum metrology. It is suggested that spin cat states can be generated by adiabatic evolution. However, due to the limited coherence time, the adiabatic process may be too slow to be practical. To speed up the state generation, we propose to use machine optimization to generate desired spin cat states. Our proposed scheme relies only on experimentally demonstrated one-axis twisting interactions with piecewise time-modulation of rotations designed via machine optimization. The required evolution time is much shorter tha…
Given a source of two coherent state superpositions with small separation in a traveling wave optical setting, we show that by interference and balanced homodyne measurement it is possible to conditionally prepare a symmetrically placed superposition of coherent states around the origo of the phase space. The separation of the coherent states in the superposition will be amplified during the process.
Optimizing decoherence in the generation of optical Schrödinger cat states
通过利用腔体Rydberg电磁诱导透明性，研究者提出了一种生成高平均光子数的光Schrödinger猫态的方法，并通过调节光子损失强度以减少退相干。
The problem of photon adding and subtracting is studied, using conditional output measurement on a beam splitter. It is shown that for various classes of states the corresponding photon-added and -subtracted states can be prepared. Analytical results are presented, with special emphasis on photon-added and -subtracted squeezed vacuum states, which are found to represent two different types of Schroedinger-cat-like states. Effects of realistic photocounting and Fock-state preparation are discussed.
Nonreciprocal Generation of Schrödinger Cat State Induced by Topology
本文提出在一维微腔阵列中利用拓扑保护手性模式激发，实现边缘腔薛定谔猫态的方向选择性非互易产生，并可通过拓扑相变开关控制。
Generation of Four-Component Schrödinger Cat States via Floquet Engineering in a Hybrid Ferromagnet-Superconductor System
针对固态平台难以制备四分量薛定谔猫态的问题，提出混合铁磁体-超导体系统中的 Floquet 工程方案，并证明在退相干下仍可高保真生成该态。
Macroscopic entangled cat states not only are significant in the demonstration of the fundamentals of quantum physics, but also have wide applications in modern quantum technologies such as continuous-variable quantum information processing and quantum metrology. Here we propose a scheme for generation of macroscopic entangled cat states in a molecular cavity-QED system, which is composed of an organic molecule (including electronic and vibrational states) coupled to a single-mode cavity field. By simultaneously modulating the resonance frequencies of the molecular vibration and the cavity fie…
A recursive method for producing path-entangled states of light is presented. These states may find applications in quantum lithography and high-precision interferometric measurements. The required resources are single-photon sources, linear optics components, and photodetectors. Adding a quantum memory greatly enhances the yield in comparison with the previously known schemes.
Chiral-cat-state generation via the Sagnac-Fizeau effect
本文提出利用旋转谐振器中的Sagnac-Fizeau效应，通过二能级原子与CW/CCW模式的色散耦合及条件旋转演化和原子投影测量，分别在CW模式生成猫态、在CCW模式生成相干态，并分析了其量子相干性与耗散影响。
We present an algorithm to reliably generate various quantum states critical to quantum error correction and universal continuous-variable (CV) quantum computing, such as Schrödinger cat states and Gottesman-Kitaev-Preskill (GKP) grid states, out of Gaussian CV cluster states. Our algorithm is based on the Photon-counting-Assisted Node-Teleportation Method (PhANTM), which uses standard Gaussian information processing on the cluster state with the only addition of local photon-number-resolving measurements. We show that PhANTM can apply polynomial gates and embed cat states within the cluster. …
Loss-tolerant parallelized Bell-state generation with a hybrid cat qudit
本文提出一种利用相干光脉冲相位编码量子比特的并行贝尔态生成协议，通过XX奇偶性综合征检测并纠正光子丢失，实现容错的量子通信与计算。
Generation of bipartite mechanical cat state by performing projective Bell state measurement
提出利用投影贝尔态测量实现纠缠交换，生成四种二分体声子贝尔猫态，并基于CHSH不等式进行贝尔不等式测试，为连续变量量子网络处理器提供新方法。
Linear-optical generation of hybrid GKP entanglement from small-amplitude cat states
本文提出利用小振幅猫态生成GKP量子位与光子数态之间的混合纠缠态，通过线性光学元件和相干测量实现高效制备，扩展至混合量子纠错。
We investigate the dynamics of a two-level atom in a cavity filled with a nonlinear medium. We show that the atom-field detuning $δ$ and the nonlinear parameter $χ^{(3)}$ may be combined to yield a periodic dynamics and allowing the generation of almost exact superpositions of coherent states ({\sl Schrödinger} cats). By analysing the atomic inversion and the field purity, we verify that any initial atom-field state is recovered at each revival time, and that a coherent field interacting with an excited atom evolves to a superposition of coherent states at each collapse time. We show that a mi…
Quantum states are important resources and their preparations are essential prerequisites to all quantum technologies. However, they are extremely fragile due to the inevitable dissipations. Here, an all-optical generation of a deterministic squeezed Schr$\ddot{\mathrm{o}}$dinger-cat state based on dissipation is proposed. Our system is based on the Fredkin-type interaction between three optical modes, one of which is subject to coherent two-photon driving and the rest are coherent driving. We show that an effective degenerate three-wave mixing process can be engineered in our system, which ca…
We discuss general properties of the equilibrium state of parametric down-conversion in superconducting quantum circuits with detunings and Kerr anharmonicities, in the strongly nonlinear regime. By comparing moments of the steady state and those of a Schrödinger cat, we show that true Schrödinger cats cannot survive in the steady state if there is any single-photon loss. A delta-function 'cat-like' steady-state distribution can be formed, but this only exists in the limit of an extremely large nonlinearity. The steady state is a mixed state, which is more complex than a mixture or linear comb…
We present an efficient method to generate a Greenberger-Horne-Zeilinger (GHZ) entangled state of three cat-state qubits (cqubits) via circuit QED. The GHZ state is prepared with three microwave cavities coupled to a superconducting transmon qutrit. Because the qutrit remains in the ground state during the operation, decoherence caused by the energy relaxation and dephasing of the qutrit is greatly suppressed. The GHZ state is created deterministically because no measurement is involved. Numerical simulations show that high-fidelity generation of a three-cqubit GHZ state is feasible with prese…
In this paper, we examine the effects of the gravitational field on the dynamical evolution of the cavity-field entropy and the creation of the Schrodinger-cat state in the Jaynes-Cummings model. We consider a moving two-level atom interacting with a single mode quantized cavity-field in the presence of a classical homogeneous gravitational field. Based on an su(2) algebra, as the dynamical symmetry group of the model, we derive the reduced density operator of the cavity-field which includes the effects of the atomic motion and the gravitational field. Also, we obtain the exact solution and th…
We propose a method to generate an optical Schrödinger-cat-like state in a cavity in a substantial decoherence regime. Even when the cavity decay rate is considerably large, a cat-like state can be generated in a laser-like setting if the gain for the field is larger than the loss. Under the condition that opposite-phase atomic dipoles repeatedly traverse the cavity, the cavity field converges to a squeezed vacuum state in a steady state. A Schrödinger-cat-like state is then generated when a single photon decay occurs. The phase-space distribution of the cat state can be revealed in homodyne d…
Fast generation of Schrödinger cat states in a Kerr-tunable superconducting resonator
针对三维腔中薛定谔猫态的可扩展性与可控性难题，提出通过快速调制克尔非线性在共面超导电路中生成存储猫态的新方法，96ns内实现89.1%保真度的双组分猫态，为芯片级玻色量子处理器构建提供新路径。
Deterministic generation of cat states with more than $100$ photons under dissipation
利用混合量子比特-玻色子系统的动力学不变量，在厄米或非厄米含时哈密顿量下，通过通用量子控制理论，从真空态确定性演化出平均光子数超过120的猫态，厄米情形完美生成，非厄米情形保真度超过0.962。
We propose a method for the fast generation of nonclassical ground states of the Rabi model in the ultrastrong and deep-strong coupling regimes via the shortcuts-to-adiabatic (STA) dynamics. The time-dependent quantum Rabi model is simulated by applying parametric amplification to the Jaynes-Cummings model. Using experimentally feasible parametric drive, this STA protocol can generate large-size Schrödinger cat states, through a process that is 10 times faster compared to adiabatic protocols. Such fast evolution increases the robustness of our protocol against dissipation. Our method enables o…
Until now, Schrödinger's cat states are generated by subtracting single photons from the whole bandwidth of squeezed vacua. However, it was pointed out recently that the achievable purities are limited in such method (J. Yoshikawa, W. Asavanant, and A. Furusawa, arXiv:1707.08146 [quant-ph] (2017)). In this paper, we used our new photon subtraction method with a narrowband filtering cavity and generated a highly pure Schrödinger's cat state with the value of $-0.184$ at the origin of the Wigner function. To our knowledge, this is the highest value ever reported without any loss corrections. The…
Measurement-induced generation of Schrödinger cat states in cavity QED
该研究在腔-QED系统中提出结合相干驱动、色散原子-腔相互作用和原子后选择的测量方案，可实验可行地产生抗中等腔耗散的薛定谔猫态，无需强光学非线性或工程化耗散。
A scheme is proposed to prepare squeezed states and Schrödinger cat-like states of the collective spin degrees of freedom associated with a pair of ground states in an atomic ensemble. The scheme uses an effective Jaynes-Cummings interaction which can be provided by excitation of the atoms to Rydberg states and an effective J_x interaction implemented by a resonant Raman coupling between the atomic ground states. Both dynamical evolution with a constant Hamiltonian and with adiabatic variation of the two interaction terms are studied. We show that by the application of further resonant laser f…
Thermal-dephasing-tolerant generation of Schrödinger cat states with Rydberg dressed blockade
本研究提出基于里德堡缀饰原子的抗热退相介观纠缠态生成方案，将逻辑态编码在缀饰态上，使多体纠缠相干寿命提升至里德堡态编码的约3倍，为大规模量子计算与多体里德堡量子模拟提供理论支撑。
With the reliance in the processing of quantum information on a cold trapped ion, we analyze the entanglement entropy in the ion-field interaction with pair cat states. We investigate a long-living entanglement allowing the instantaneous position of the center-of-mass motion of the ion to be explicitly time dependent. An analytic solution for the system operators is obtained. We show that different nonclassical effects arise in the dynamics of the population inversion, depending on the initial states of the vibrational motion. We study in detail the entanglement degree and demonstrate how the …
Macroscopic cat states have been widely studied to illustrate fundamental principles of quantum physics as well as their application in quantum information processing. In this paper, we propose a quantum speedup method for adiabatic creation of cat states in a Kerr nonlinear resonator via gradient-descent optimal adiabatic control. By simultaneously adiabatic tuning the the cavity detuning and driving field strength, the width of minimum energy gap between the target trajectory and non-adiabatic trajectory can be widen, which allows us to speed up the evolution along the adiabatic path. Compar…
We propose a scheme to generate macroscopic Schrödinger-cat states in a quantum harmonic oscillator (electromagnetic field or mechanical resonator) coupled to a quantum bit (two-level system) via a conditional displacement mechanism. By driving the qubit monochromatically, the oscillation of the qubit state modifies the effective frequency of the driving force acting on the oscillator, and a resonant or near-resonant driving on the oscillator can be achieved. The displacement of the oscillator is then significantly enhanced due to the small detuning of the driving force and can exceed that of …
Efficient optical cat state generation using squeezed few-photon superposition states
本文提出利用压缩的少光子叠加态高效生成高保真度光学猫态，通过线性光学协议实现高保真度和高容忍性。
Optical Schrödinger cat states generation using cubic phase resource state and beamsplitter
本文提出一种基于非对称分束器和三次相位资源态的光学方案，通过零差测量产生具有可控压缩度的薛定谔猫态，并进行了半经典分析与效率比较。
We investigate a superadiabatic scheme to produce a cat state in a bosonic Josephson junction in absence and presence of particle losses. The generation scheme is based on shortcuts to adiabaticity and strongly relies on the parity conservation. The parity conservation also ensures that the produced state is a superposition of cat states with various sizes, i.e., a "cats state". Parity is also the quantity to be measured in order to utilize the produced state in interferometry. The generation scheme still works even if a number of particle losses during generation are substantial.
We theoretically propose a method for on-demand generation of traveling Schrödinger cat states, namely, quantum superpositions of distinct coherent states of traveling fields. This method is based on deterministic generation of intracavity cat states using a Kerr-nonlinear parametric oscillator (KPO) via quantum adiabatic evolution. We show that the cat states generated inside a KPO can be released into an output mode by controlling the parametric pump amplitude dynamically. We further show that the quality of the traveling cat states can be improved by using a shortcut-to-adiabaticity techniq…
We propose a quantum speedup method for adiabatic generation of cat states in bosonic Josephson junctions via shortcuts to adiabaticity. We apply approximated counter-diabatic driving to a bosonic Josephson junction using the Holstein-Primakoff transformation. In order to avoid the problem of divergence in counter-diabatic driving, we take finite-size corrections into account. The resulting counter-diabatic driving is well-defined over whole processes. Schedules of the counter-diabatic driving consist of three steps; the counter-diabatic driving in the disordered phase, smoothly and slowly app…
Magnon cat state represents a macroscopic quantum superposition of collective magnetic excitations of large number spins that not only provides fundamental tests of macroscopic quantum effects but also finds applications in quantum metrology and quantum computation. In particular, remote generation and manipulation of Schrödinger cat states are particularly interesting for the development of long-distance and large-scale quantum information processing. Here, we propose an approach to remotely prepare magnon even/odd cat states by performing local non-Gaussian operations on the optical mode tha…
We introduce a simple, physically-motivated variational ground state for the quantum Rabi model, and demonstrate that it provides a high-fidelity approximation of the true ground state in all parameter regimes (including intermediate and strong coupling regimes). Our variational state is constructed using Gaussian cavity states and nonorthogonal qubit pointer states, and contains only three variational parameters. We use our state to develop a heuristic understanding of how the ground state evolves with increasing coupling, and find a previously unexplored regime where the ground state corresp…
The high fidelity generation of strongly entangled states of many particles, such as cat states, is a particularly demanding challenge. One approach is to drive the system, within a certain final time, as adiabatically as possible, in order to avoid the generation of unwanted excitations. However, excitations can be generated also by the presence of dissipative effects such as dephasing. Here we compare the effectiveness of Local Adiabatic and the FAst QUasi ADiabatic protocols in achieving a high fidelity for a target superposition state both with and without dephasing. In particular we consi…
We study suppression of nonadiabatic transitions during adiabatic generation of a cat-like state (a superposition of different size cat states) and a spin squeezed state in a bosonic Josephson junction. In order to minimize the adiabatic error, we use quantum adiabatic brachistochrone, which enables us to track a geometrically efficient path in parameter space under given conditions without requiring additional terms. For creation of a cat-like state, divergence of the quantum geometric tensor associated with gap closing at the critical point is avoided because of the parity conservation. The …
Schrödinger cat states are useful for many applications, ranging from quantum information processing to high-precision measurements. In this paper we propose a conceptually new method for creating such cat states, based on photon-assisted Landau-Zener-Stückelberg interferometry in a hybrid system consisting of a qubit coupled to a photon cavity. We show that by initializing the qubit in one of its basis states, performing three consecutive sweeps of the qubit energy splitting across the 1-photon resonance, and finally projecting the qubit to the same basis state, the parity of the photon field…
We discuss the possibility of generating and detecting, by a tomographic reconstruction of the Wigner function, a macroscopic superposition of two coherent states. The superposition state is created using a conditioned measurement on the polarisation of a probe photon entangled to a coherent state. The entanglement is obtained using a Kerr cell inserted in a Mach-Zender interferometer. Some hint about generation of GHZ states is given as well.
Quantum entanglement involving coherent superpositions of macroscopically distinct states is among the most striking features of quantum theory, but its realization is challenging, since such states are extremely fragile. Using a programmable quantum simulator based on neutral atom arrays with interactions mediated by Rydberg states, we demonstrate the deterministic generation of 'Schrödinger cat' states of the Greenberger-Horne-Zeilinger (GHZ) type with up to 20 qubits. Our approach is based on engineering the energy spectrum and using optimal control of the many-body system. We further demon…
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