L. Arevalo Aguilar, H. Moya-Cessa
We study the effects of counter rotating terms in the interaction of quantized light with a two-level atom, by using the method of small rotations. We give an expression for the wave function of the composed system atom plus field and point out one initial wave function that generates a quantum bit of the electromagnetic field with arbitrary amplitudes.
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Displaced Fock states of the electromagnetic field have been synthesized by overlapping the pulsed optical single-photon Fock state |1> with coherent states on a high-reflection beamsplitter and completely characterized by means of quantum homodyne tomography. The reconstruction reveals highly non-classical properties of displaced Fock states, such as negativity of the Wigner function and photon number oscillations. This is the first time complete tomographic reconstruction has been performed on a highly non-classical optical state.
Negative refraction index manipulated by a displaced squeezed Fock state in the mesoscopic dissipative left-handed transmission line
研究介观耗散左手传输线中由平移压缩Fock态与耗散调控负折射率，揭示量子特性以促进微波频率下的微型化应用。
Realistic continuous-variable quantum teleportation using a displaced Fock state channel
本文研究基于位移福克态资源的连续变量量子隐形传态，发现其对单模输入场的平均保真度仅达经典阈值，并分析了贝尔测量误差和光纤损耗等退相干因素对保真度的影响及参数优化条件。
Analyzing performance of $f$-deformed displaced Fock state in continuous-variable quantum teleportation
本文研究了非高斯资源在连续变量量子隐形传态中的成功概率，推导了基于$f$-变形平移Fock态等纠缠信道的解析表达式，发现非线性替换能超越阈值提升保真度，且光子扣除平移Fock态展现最大传输效率。
Boson sampling is a specific quantum computation, which is likely hard to implement efficiently on a classical computer. The task is to sample the output photon number distribution of a linear optical interferometric network, which is fed with single-photon Fock state inputs. A question that has been asked is if the sampling problems associated with any other input quantum states of light (other than the Fock states) to a linear optical network and suitable output detection strategies are also of similar computational complexity as boson sampling. We consider the states that differ from the Fo…
The spin-boson model is analytically studied using displaced Fock states (DFS) without discretization of the continuum bath. In the orthogonal displaced Fock basis, the ground-state wavefunction can be systematically improved in a controllable way. Interestingly, the zeroth-order DFS reproduces exactly the well known Silbey-Harris results. In the framework of the second-order DFS, the magnetization and the entanglement entropy are exactly calculated. It is found that the magnetic critical exponent $β$ is converged to $0.5$ in the whole sub-Ohmic bath regime $0<s<1$, compared with that by the e…
Nonclassical properties of photon added and subtracted displaced Fock states have been studied using various witnesses of lower- and higher-order nonclassicality. Compact analytic expressions are obtained for the nonclassicality witnesses. Using those expressions, it is established that these states and the states that can be obtained as their limiting cases (except coherent states) are highly nonclassical as they show the existence of lower- and higher-order antibunching and sub-Poissonian photon statistics, in addition to the nonclassical features revealed through the Mandel $Q_M$ parameter,…
Non-Gaussian and nonclassical states and processes are already found to be important resources for performing various tasks related to quantum gravity and quantum information processing. The effect of non-Gaussianity inducing operators on the nonclassicality of quantum states has also been studied rigorously. Considering these facts, a quantitative analysis of the nonclassical and non-Gaussian features is performed here for photon added displaced Fock state, as a test case, using a set of measures like entanglement potential, Wigner Yanese skew information, Wigner logarithmic negativity and re…
Quantum phase properties of photon added and subtracted displaced Fock states (and a set of quantum states which can be obtained as the limiting cases of these states) are investigated from a number of perspectives, and it is shown that the quantum phase properties are dependent on the quantum state engineering operations performed. Specifically, the analytic expressions for quantum phase distributions and angular $Q$ distribution as well as measures of quantum phase fluctuation and phase dispersion are obtained. The uniform phase distribution of the initial Fock states is observed to be trans…
Detecting Nonclassicality and quantum non-Gaussianity of photon subtracted displaced Fock state
本文利用多种测度定量研究了光子扣除平移Fock态的非经典性与量子非高斯性，发现Fock参数的作用强于光子扣除数，并证明Wigner负性仅能由高效率探测器揭示。
This paper presents some results on some aspects of the two-level atom interacting with a single-mode with the privileged field mode being in the squeezed displaced Fock state (SDFS). The exact results are employed to perform a careful investigation of the temporal evolution of the atomic inversion, entropy and phase distribution. It is shown that the interference between component states leads to non-classical oscillations in the photon number distribution. At mid revival time the field is almost in the pure state. We have briefly discussed the evolution of the Q function of the cavity field.…
Coherent states and their generalisations, displaced Fock states, are of fundamental importance to quantum optics. Here we present a direct observation of a classical analogue for the emergence of these states from the eigenstates of the harmonic oscillator. To this end, the light propagation in a Glauber-Fock waveguide lattice serves as equivalent for the displacement of Fock states in phase space. Theoretical calculations and analogue classical experiments show that the square-root distribution of the coupling parameter in such lattices supports a new family of intriguing quantum correlation…
The observation of genuine quantum features of nano-mechanical motion is a key goal for both fundamental and applied quantum science. To this end, a promising approach is the stabilization of nonclassical features in the presence of dissipation, by means of the tunable coupling with a photonic environment. Here we present a scheme that combines dissipative squeezing with a mechanical nonlinearity to stabilize arbitrary approximations of (displaced) mechanical Fock state of any number. We consider an optomechanical system driven by three control lasers--at the cavity resonance and at the two me…
Various nonclassical and quantum phase properties of photon added then subtracted displaced Fock state have been examined systematically and rigorously. Higher-order moments of the relevant bosonic operators are computed to test the nonclassicality of the state of interest, which reduces to various quantum states (having applications in quantum optics, metrology and information processing) in different limits ranging from the coherent (classical) state to the Fock (most nonclassical) states. The nonclassical features are discussed using Klyshko's, Vogel's, and Agarwal-Tara's criteria as well a…
We find a tight upper bound for the classical capacity of quantum thermal noise channels that is within $1/\ln 2$ bits of Holevo's lower bound. This lower bound is achievable using unentangled, classical signal states, namely displaced coherent states. Thus, we find that while quantum tricks might offer benefits, when it comes to classical communication they can only help a bit.
We present a protocol to deterministically prepare the electromagnetic field in a large photon number state. The field starts in a coherent state and, through resonant interaction with one or few two-level systems, it evolves into a coherently displaced Fock state, without any post-selection. We show the feasibility of the scheme under realistic parameters. The presented method opens a door to reach Fock states with $n\sim100$ and optimal fidelities above $70$%, blurring the line between macroscopic and quantum states of the field.
A measure of nonclassicality of quantum states based on the volume of the negative part of the Wigner function is proposed. We analyze this quantity for Fock states, squeezed displaced Fock states and cat-like states defined as coherent superposition of two Gaussian wave packets.
The quantum discrimination of two non-coherent states draws much attention recently. In this letter, we first consider the quantum discrimination of two noiseless displaced number states. Then we derive the Fock representation of noisy displaced number states and address the problem of discriminating between two noisy displaced number states. We further prove that the optimal quantum discrimination of two noisy displaced number states can be achieved by the Kennedy receiver with threshold detection. Simulation results verify the theoretical derivations and show that the error probability of on…
Compass state: Effect of squeezing and displacement on the Fock space
研究压缩与位移对Fock空间的影响，发现所提状态与compass状态在保真度和测量方差方面表现相似，具有潜在的计量应用价值。
We derive analytical expressions for the single mode quantum field state at the individual output ports of a beam splitter when a single-photon Fock state and a coherent state are incident on the input ports. The output states turn out to be a statistical mixture between a displaced Fock state and a coherent state. Consequently we are able to find an analytical expression for the corresponding Wigner function. Because of the generality of our calculations the obtained results are valid for all passive and lossless optical four port devices. We show further how the results can be adapted to the…
We introduce transformation matrix connecting sets of the displaced states with different displacement amplitudes. Arbitrary pure one-mode state can be represented in new basis of the displaced number (Fock) states ( representation) by multiplying the transposed transformation matrix on a column vector of initial state. Analytical expressions of the representation of superposition of vacuum and single photon and two-mode squeezed vacuum (TMSV) are obtained. On the basis of the developed mathematical formalism, we consider the mechanism of interaction between qubits which is based on their disp…
We put forward a deterministic dissipative protocol to prepare phonon Fock states in nonlinear quantum optomechanical devices. The system is composed of a mechanical mode interacting with an optical field via radiation pressure, whereas the light mode is laser-driven in the resolved blue-sideband regime. To keep our results tractable, we have switched to an interaction picture in a displaced basis, where the effective Hamiltonian exhibits the selective photon-phonon interaction explicitly. After proper parameter adjustment and similarly to cavity-cooling schemes, the quantum evolution allows s…
We introduce a simple measure of "classicality" of pure and mixed quantum states as a maximum value of the Hilbert-Schmidt "scalar products" between the renormalized statistical operators of the state concerned and all displaced thermal states. Choosing Fock states as the reference set, we introduce the measure of "anticlassicality". Both measures are illustrated for the Fock, coherent phase, and generic mixed Gaussian states. Gaussian states are shown to be the closest to thermal states possessing the same degree of quantum purity. On the contrary, Fock states appear to be more close to mixed…
Quantum signatures and semiclassical limitations in the transmission of Fock states
本文研究了福克态通过倒置振子势垒的传输，探讨了经典方法在捕捉量子干涉方面的局限性，并指出塞曼方法无法描述Wigner函数负性带来的短时间平台效应。
Nonlinear Compton scattering in a quantized pump field
本研究建立了单模量子场驱动的非线性康普顿散射全量子理论，分析了有限福克态泵浦的光谱特性，给出弱损耗区域的近似形式，并揭示压缩相干光的压缩角对高能发射的调控作用。
In this paper, the well-known Silbey-Harris (SH) polaron ansatz for the spin-boson model is improved by adding orthogonal displaced Fock states. The obtained results for the ground state in all baths converge very quickly within finite displaced Fock states and corresponding SH results are corrected considerably. Especially for the sub-Ohmic spin-boson model, the converging results are obtained for 0 < s < 1/2 in the fourth-order correction and very accurate critical coupling strengths of the quantum phase transition are achieved. Converging magnetization in the biased spin-boson model is also…
The construction of a class of unitary operators generating linear superpositions of generalized coherent states from the ground state of a quantum harmonic oscillator is reported. Such a construction, based on the properties of a new ad hoc introduced set of hermitian operators, leads to the definition of new basis in the oscillator Hilbert space, extending in a natural way the displaced Fock states basis. The potential development of our method and our results is briefly outlined.
In quantum photonics, threshold detectors, distinguishing between vacuum and one or more photons, such as superconducting nanowires and avalanche photodiodes, are routinely used to measure Fock and Gaussian states of light. Despite being the standard measurement scheme, there is no general closed form expression for measurement probabilities with threshold detectors, unless accepting coarse approximations or combinatorially scaling summations. Here, we present new matrix functions to fill this gap. We develop the Bristolian and the loop Torontonian functions for threshold detection of Fock and…
Generating Fock state exceeding 10000 excitations with near unit fidelity by adaptive generalized-parity measurement
提出一种自适应广义宇称测量协议，通过重复测量辅助量子比特并自适应更新测量间隔，将大相干态转换为光子数高达10^4的大Fock态，平均保真度约80%，且高保真度概率约35%。
We develop a technique for generating multi-photon nonclassical states via interference between coherent and Fock states using quantum catalysis. By modulating the coherent field strength, the number of catalyst photons and the ratio of the beam splitter upon which they interfere, a wide range of nonclassical phenomena can be created, including squeezing of up to 1.25 dB, anti- and super-bunched photon statistics and states exhibiting over 90% fidelity to displaced coherent superposition states. We perform quantum catalysis experimentally, showing tunability into the nonclassical regime. Our p…
We study the compression of n quantum systems, each prepared in the same state belonging to a given parametric family of quantum states. For a family of states with f independent parameters, we devise an asymptotically faithful protocol that requires a hybrid memory of size (f/2)log(n), including both quantum and classical bits. Our construction uses a quantum version of local asymptotic normality and, as an intermediate step, solves the problem of compressing displaced thermal states of n identically prepared modes. In both cases, we show that (f/2)log(n) is the minimum amount of memory neede…
For the visualization of quantum states, the approach based on Wigner functions can be very effective. Homodyne detection has been extensively used to obtain the density matrix, Wigner functions and tomographic reconstructions of optical fields for many thermal, coherent or squeezed states. Here, we use time-domain optical homodyne tomography for the quantum state recognition and reconstruction of the femtosecond optical field from a nonequilibrium superradiant coherent electron-hole state formed in a semiconductor laser structure. We observe severe deviations from the Poissonian statistics of…
Lower- versus higher-order nonclassicalities for a coherent superposed quantum state
本文研究相干态上叠加湮灭与产生算符所得量子态的非经典性，发现高阶判据比低阶条件更能有效检测非经典性。
The characteristics of nonstatic quantum light waves in the coherent state in a static environment is investigated. It is shown that the shape of the wave varies periodically as a manifestation of its peculiar properties of nonstaticity like the case of the Fock-state analysis for a nonstatic wave. A belly occurs in the graphic of wave evolution whenever the wave is maximally displaced in the quadrature space, whereas a node takes place every time the wave passes the equilibrium point during its oscillation. In this way, a belly and a node appear in turn successively. Whereas this change of wa…
The large available Hilbert space and high coherence of cavity resonators makes these systems an interesting resource for storing encoded quantum bits. To perform a quantum gate on this encoded information, however, complex nonlinear operations must be applied to the many levels of the oscillator simultaneously. In this work, we introduce the Selective Number-dependent Arbitrary Phase (SNAP) gate, which imparts a different phase to each Fock state component using an off-resonantly coupled qubit. We show that the SNAP gate allows control over the quantum phases by correcting the unwanted phase …
The interaction of a two-level atom with a single-mode quantized field is one of the simplest models in quantum optics. Under the rotating wave approximation, it is known as the Jaynes-Cummings model and without it as the Rabi model. Real-world realizations of the Jaynes-Cummings model include cavity, ion trap and circuit quantum electrodynamics. The Rabi model can be realized in circuit quantum electrodynamics. As soon as nonlinear couplings are introduced, feasible experimental realizations in quantum systems are drastically reduced. We propose a set of two photonic lattices that classically…
We consider novel implementation of quantum teleportation protocol of unknown qubit by superposition of displacement operators with equal modulo but opposite in sign amplitudes. Entangled hybrid state with coherent components of small amplitude is used as quantum channel. Coherent components of the quantum channel displace the teleported qubit at the same absolute but opposite in sign values, so that any information about amount by which the qubit is displaced is lost despite the fact that one of these events has definitely occurred. Alice unambiguously distinguishes her measurement outcomes a…
We present a quantum phase space model of Bose-Einstein condensate (BEC) in a double well potential. In a two-mode Fock-state analysis we examine the eigenvectors and eigenvalues and find that the energy correlation diagram indicates a transition from a delocalized to a fragmented regime. Phase space information is extracted from the stationary quantum states using the Husimi distribution function. It is shown that the quantum states are localized on the known classical phase space orbits of a nonrigid physical pendulum, and thus the novel phase space characteristics of a nonrigid physical pen…
Differential hierarchy of the Husimi representation
本文通过将 Husimi 表示的正定性条件局部化，建立了基于导数的微分层级，并给出等价的代数行列式判据，揭示了算子秩与正定性在相空间中的局部性。
We interpret the Holographic Conjecture in terms of quantum bits (qubits). N-qubit states are associated with surfaces that are punctured in N points by spin networks' edges labeled by the spin-1/2 representation of SU(2), which are in a superposed quantum state of spin "up" and spin "down". The formalism is applied in particular to de Sitter horizons, and leads to a picture of the early inflationary universe in terms of quantum computation. A discrete micro-causality emerges, where the time parameter is being defined by the discrete increase of entropy. Then, the model is analysed in the fram…
Single photons are the natural link between the nodes of a quantum network: they coherently propagate and interact with many types of quantum bits including natural and artificial atoms. Ideally, one atom should deterministically control the state of a photon and vice-versa. The interaction between free space photons and an atom is however intrinsically weak and many efforts have been dedicated to develop an efficient interface. Recently, it was shown that the propagation of light can be controlled by an atomic resonance coupled to a cavity or a single mode waveguide. Here we demonstrate that …
Squeezing Quantum States in Three-Dimensional Twisted Crystals
针对三维扭曲晶体中不相称周期竞争导致布洛赫波原理失效的问题，提出用自由粒子涡旋态福克空间的压缩相干态替代频谱拥挤的布洛赫能带结构，揭示科里奥利力对非常规相空间动力学及边缘态结构的关键作用。
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