We study the use of squeezed light for qubit coherent control and compare it with the coherent state control field case. We calculate the entanglement between a short pulse of resonant squeezed light and a two-level atom in free space and the resulting operation error. We find that the squeezing phase, the phase of the light field and the atomic superposition phase, all determine whether atom-pulse mode entanglement and the gate error are enhanced or suppressed. However, when averaged over all possible qubit initial states, the gate error would not decrease by a practicably useful amount and would in fact increase in most cases. We discuss the possibility of measuring the increased gate error as a signature of the enhancement of entanglement by squeezing.
Dispersive interactions of matter qubits with bright squeezed light in a high-Q cavity is studied. Numerical simulation shows that higher fidelity of operations to obtain a certain phase shift of the pulse through the dispersive light-matter interaction may be reached using bright squeezed light than that using bright coherent light.
We study the relation between the sudden death and revival of the entanglement of two qubits in a common squeezed reservoir, and the normal decoherence, by getting closer to the Decoherence Free Subspace and calculating the effect on the death and revival times.
We use a single squeezed state to represent a qubit, which can be coherently processed in a deconvolution picture (DP) in the presence of noise. We avail ourselves of the fact that when evolution is governed by a quadratic dissipative equation, there exists a basis of squeezed states that evolves to another basis of such states in the DP. An operator acts as an impurity filter, restoring the coherence lost from the inexorable interactions of the qubit with its surroundings.
Squeezed state of light is one of the important subjects in quantum optics which is generated by optical nonlinear interactions. In this paper, we especially focus on qubit like entangled squeezed states (ESS's) generated by beam splitters, phase-shifter and cross Kerr nonlinearity. Moreover the Wigner function of two-mode qubit and qutrit like ESS are investigated. We will show that the distances of peaks of Wigner functions for two-mode ESS are entanglement sensitive and can be a witness for entanglement. Like the qubit cases, monogamy inequality is fulfilled for qutrit like ESS. These trend…
The decoherence of two initially entangled qubits in a squeezed vacuum cavity has been investigated exactly. The results show that, first, in principle, the disentanglement time decreases with the increasing of squeeze parameter r, due to the augmenting of average photon number of every mode in squeezed vacuum cavity. Second, there are entanglement revivals after complete disentanglement for the case of even parity initial Bell state, while there are entanglement decrease and revival before complete disentanglement for the case of odd parity initial Bell state. The results are quite different …
There have recently been interests in transferring entanglement between two quantum systems in different Hilbert spaces. In particular, the study of entanglement transfer from a continuous-variable to a qubit system has a primary importance due to practical implications. A continuous-variable system easily propagates entanglement while a qubit system is easy to manipulate. We investigate conditions to entangle two two-level atoms for a broad-band two-mode squeezed field driving the cavities where the atoms are.
We consider the p-ordered characteristic function and its Fourier transform, the quasidistribution function, of squeezed coherent photons in a thermal state of photons and calculate the mean number and number variance of squeezed coherent photons. All the properties calculated from the previous characteristic function can be used to calculate said properties for photons in a thermal state of squeezed coherent photons via a parametric transformation. In particular, one can obtain the mean number and number variance via the parametric transformation.
We present a scheme for achieving amplification of the displacement of the mirror in optomechanical cavity using single-photon postselection where the mirror is initially prepared in squeezed coherent state. The amplification depends on the enhanced fluctuations of the squeezed coherent state, and it is is caused by the noncommutativity of quantum mechanics relying on the squeezed coherent state, which can not be explained by the standard weak measurement [1,25].
We consider the equilibrium thermal state of photons and determine the mean number and number variance of squeezed coherent photons. We use an integral representation for electro-magnetic radiation applicable both to systems in equilibrium and to systems in nonequilibrium to determine the spectral function of the radiation. The system considered is in thermal equilibrium and we find that the squeezed coherent photons are at a higher temperature than the photons themselves. Also, as expected, the mean number of squeezed coherent photons is greater than that of photons.
A quantum superposition of two coherent states of light with small amplitude can be obtained by subtracting a photon from a squeezed vacuum state. In experiments this preparation can be made conditioned on the detection of a photon in the field from a squeezed light source. We propose and analyze an extended measurement strategy which allows generation of high fidelity coherent state superpositions with larger amplitude.
We introduce the set of $n$-photon coherent states and the set of $n$-photon squeezed coherent states and study their collapse and revival and compare their behavior with the collapse and revival of the corresponding zero-photon coherent states and zero-photon squeezed coherent states, respectively. The set of $n$-photon squeezed coherent states ($n=0,1,2,\cdots$) forms a basis of the Hilbert state of photons and may be of some interest. We notice that the presence of a few extra photons in the $n$-photon states as compared to the corresponding zero-photon states makes a large difference in th…
We theoretically investigate the phase sensitivity with parity detection on a Mach-Zehnder interferometer with a coherent state combined with a photon-added squeezed vacuum state. When the phase shift approaches zero, the squeezed vacuum state is indeed the optimal state within a constraint on the average number of photons. However, when the phase shift to be estimated slightly deviates from zero, the optimal state is neither the squeezed vacuum state nor the photon-subtracted squeezed vacuum state, but the photon-added squeezed vacuum state when they carry many photons. Finally, we show that …
Using the f-deformed oscillator formalism, we introduce two types of squeezed coherent states for a Morse potential system (Morse-like squeezed coherent states) through the following definitions: i) as approximate eigenstates of a linear combination of f-deformed ladder operators and ii) as deformed photon-subtracted coherent states. For the states thus constructed we analyze their statistical properties, their uncertainty relations, and their temporal evolution on phase space.
A state in a d-dimensional Hilbert space can be simulated by a state defined in a different dimension with high fidelity. We assess how faithfully such the approximated state can perform quantum protocols, using an example of the squeezed coherent superposition state which was recently experimentally generated.
We construct semiclassical solutions of the symplectically covariant Schroedinger phase-space equation rigorously studied in a previous paper; we use for this purpose an adaptation of Littlejohn's nearby-orbit method. We take the opportunity to discuss in some detail the so fruitful notion of squeezed coherent state and the action of the metaplectic group on these states.
A closed form expression for the higher-power coherent states (eigenstates of $a^{j}$) is given. The cases j=3,4 are discussed in detail, including the time-evolution of the probability densities. These are compared to the case j=2, the even- and odd-coherent states. We give the extensions to the "effective" displacement-operator, higher-power squeezed states and to the ladder-operator/minimum-uncertainty, higher-power squeezed states. The properties of all these states are discussed.
Microwave squeezing represents the ultimate sensitivity frontier for superconducting qubit measurement. However, observation of enhancement has remained elusive, in part because integration with conventional dispersive readout pollutes the signal channel with antisqueezed vacuum. Here we induce a stroboscopic light-matter coupling with superior squeezing compatibility, and observe an increase in the room-temperature signal-to-noise ratio of 24%. Squeezing the orthogonal phase controls measurement backaction, slowing dephasing by a factor of 1.8. This protocol enables the practical use of micro…
In this paper we investigate the security of continuous variable BB84 quantum key distribution protocol using single photon added then subtracted squeezed coherent state SPASSCS. It's found that the SPASSCS is a non-Gaussian and nonclassical state. Its non-Gaussianity and non-classicality are exhibited via the Wigner function. It's shown that the proposed state is generally robust against the eavesdropping strategies, such as intercept-resend attack and superior channel attack. Further, a comparative study has proved the strong efficiency of the proposed state over coherent state, squeezed coh…
The main aim of the paper is to present the analytical solution of the Belavkin quantum filtering equation for damped harmonic oscillator being initially in the squeezed coherent state for diffusion observation with complex white noise. The comparison of the a priori and a posteriori mean value of the optical quadrature operators and the photon number operator is given.
We propose a method of an improving quality of a ring cavity which is imperfect due to non-unit mirror reflectivity. The method is based on using squeezed states of light pulses illuminating the mirror and gradual homodyne detection of a radiation escaping from the cavity followed by single displacement and single squeezing operation performed on the released state. We discuss contribution of this method in process of storing unknown coherent and known squeezed state and generation of squeezing in the optical ring cavities.
The Gottesman-Kitaev-Preskill (GKP) encoding of a qubit within an oscillator provides a number of advantages when used in a fault-tolerant architecture for quantum computing, most notably that Gaussian operations suffice to implement all single- and two-qubit Clifford gates. The main drawback of the encoding is that the logical states themselves are challenging to produce. Here we present a method for generating optical GKP-encoded qubits by coupling an atomic ensemble to a squeezed state of light. Particular outcomes of a subsequent spin measurement of the ensemble herald successful generatio…
Using the Paul Trap as a model, we point out that the same wave functions can be variously coherent or squeezed states, depending upon the system they are applied to.
We propose a protocol that enables strong coupling between a flux qubit and the quantized motion of a magnetized nanomechanical cantilever. The flux qubit is driven by microwave fields with suitable parameters to induce sidebands, which will lead to the desired coupling. We show that the nanomechanical modes can be cooled to the ground states and the single-mode squeezed vacuum states can be generated via fast dissipation of the flux qubit. In our scheme, the qubit decay plays a positive role and can help drive the system to the target states.
The time evolution of a squeezed coherent state conditioned by the results of a single and double heterodyne measurement is discussed. The mean values of quadratures as well as the dynamics of quadrature uncertainties have been obtained within the framework of the theory of continuous measurements based on filtration equations. It has been found that while the mean values depend on the measured noise, the uncertainties in the optical quadratures are deterministic. Explicit solutions for the latter have been provided. Finally, a time development of the squeeze parameter for the posterior squeez…
In this work, we have applied the integrals of motion method in a nonunitary approach and so obtained the time-dependent displacement and squeezed parameters of the coherent squeezed states (CSS). On its turn, CSS for one-dimensional systems with general time-dependent quadratic Hamiltonian are constructed. We discuss the properties of these states, in particular, minimization of uncertainty relation and transition probabilities. As an application, we calculate the CSS of an oscillator with a time-dependent frequency and shown that the solution can be obtained from these well-known Mathieu's e…
We demonstrate how to create maximal entanglement between two qubits that are encoded in two spectrally distinct solid-state quantum emitters embedded in a waveguide interferometer. The optical probe is provided by readily accessible squeezed light, generated by parametric down-conversion. By continuously illuminating the emitters, the photon scattering and incremental path-erasure builds up entanglement. Our method does not require perfectly identical emitters, and accommodates spectral variations due to the fabrication process. Furthermore, for some line-width and energy ratios, the entangle…
Fisher-Information Recovery in Superconducting-Qubit Magnetometry with Squeezed-Microwave Readout
Institute of Quantum Materials and Physics, Henan Academy of Sciences（河南省科学院量子材料与物理研究所）；Department of Physics, Central China Normal University（华中师范大学物理学院）；State Key Laboratory of Mathematical Engineering and Advanced Computing（数学工程与先进计算国家重点实验室）；Quantum Information Institute, School of Physics and Laboratory of Zhongyuan Light, Zhengzhou University（郑州大学物理学院量子信息研究所与中原之光实验室）
We propose a scheme for long-distance distribution of quantum entanglement in which the entanglement between qubits at intermediate stations of the channel is established by using bright light pulses in squeezed states coupled to the qubits in cavities with a weak dispersive interaction. The fidelity of the entanglement between qubits at the neighbor stations (10 km apart from each other) obtained by postselection through the balanced homodyne detection of 7 dB squeezed pulses can reach F=0.99 without using entanglement purification, at same time, the probability of successful generation of en…
A pair of two level atoms A1A2, prepared either in a separable state or in an entangled state, interacts with a single mode of two mode squeezed cavity field while a third atomic qubit B interacts with the second mode of the squeezed field in a remote cavity. We analyze, numerically, the generation, sudden death and revival of three qubit entanglement as a function of initial entanglement of qubits A1A2 and degree of squeezing of electromagnetic field. Global negativity of partially transposed state operator is used to quantify the entanglement of three atom state. It is found that the initial…
A simple technique is used to obtain a general formula for the Berry phase (and the corresponding Hannay angle) for an arbitrary Hamiltonian with an equally-spaced spectrum and appropriate ladder operators connecting the eigenstates. The formalism is first applied to a general deformation of the oscillator involving both squeezing and displacement. Earlier results are shown to emerge as special cases. The analysis is then extended to multiphoton squeezed coherent states and the corresponding anholonomies deduced.
Using the transformations from paper I, we show that the Schrödinger equations for: (1)systems described by quadratic Hamiltonians, (2) systems with time-varying mass, and (3) time-dependent oscillators, all have isomorphic Lie space-time symmetry algebras. The generators of the symmetry algebras are obtained explicitly for each case and sets of number-operator states are constructed. The algebras and the states are used to compute displacement-operator coherent and squeezed states. Some properties of the coherent and squeezed states are calculated. The classical motion of these states is deom…
Gottesman-Kitaev-Preskill (GKP) qubit is a promising ingredient for fault-tolerant quantum computation (FTQC) in optical continuous variables due to its advantage of noise tolerance and scalability. However, one of the main problems in the preparation of the optical GKP qubit is the difficulty in obtaining the nonlinearity. Cross-Kerr interaction is one of the promising candidates for this nonlinearity. There is no existing scheme to use the cross-Kerr interaction to generate the optical GKP qubit for FTQC. In this work, we propose a generation method of the GKP qubit by using a cross-Kerr int…
The interference between coherent and squeezed vacuum light can produce path entangled states with very high fidelities. We show that the phase sensitivity of the above interferometric scheme with parity detection saturates the quantum Cramer-Rao bound, which reaches the Heisenberg-limit when the coherent and squeezed vacuum light are mixed in roughly equal proportions. For the same interferometric scheme, we draw a detailed comparison between parity detection and a symmetric-logarithmic-derivative-based detection scheme suggested by Ono and Hofmann.
We propose a scheme for generating the superposition and the entanglement of squeezed vacuum states of electromagnetical fields. The scheme involves single-photon source, single photon detector, and cross Kerr nonlinearity. The Kerr nonlinearity required for generating the superposition of squeezed vacuum states is 1/2 of that required for generating the superposition of coherent states. The proposal can also be extended to generate the entanglement states between two coherent states and that between one coherent state and one squeezed vacuum state.
We propose a hybrid quantum-classical atomic clock protocol where the interrogation of an ensemble of uncorrelated atoms in a spin-coherent state is used to feedback one (or more) spin-squeezed atomic ensembles toward their optimal phase sensitivity point. This protocol overcomes the stability of a single Ramsey clock and it reaches a Heisenberg-limited stability while avoiding non-destructive measurements. Analytical predictions are compared with numerical simulations of clocks operations including correlated 1/f local oscillator noise.
For use in calculating higher-order coherent- and squeezed- state quantities, we derive generalized generating functions for the Hermite polynomials. They are given by $\sum_{n=0}^{\infty}z^{jn+k}H_{jn+k}(x)/(jn+k)!$, for arbitrary integers $j\geq 1$ and $k\geq 0$. Along the way, the sums with the Hermite polynomials replaced by unity are also obtained. We also evaluate the action of the operators $\exp[a^j(d/dx)^j]$ on well-behaved functions and apply them to obtain other sums.
The geometric phases for standard coherent states which are widely used in quantum optics have attracted a large amount of attention. Nevertheless, few physicists consider about the counterparts of non-linear coherent states, which are useful in the description of the motion of a trapped ion. In this paper, the non-unitary and non-cyclic geometric phases for two nonlinear coherent and one squeezed states are formulated respectively. Moreover, some of their common properties are discussed respectively, such as gauge invariance, non-locality and non-linear effects. The non-linear functions have …
Theoretical analysis is given for a two-photon subtraction from a continuous wave (CW) squeezed vacuum with finite time separation between two detection events. In the CW photon subtraction process, the generated states are inevitably described by temporal mutimode states. Our approach is based on Schrödinger picture which provides mathematically simple forms and an intuitive understanding of its multimode structure. We show that, in our process, the photon subtracted squeezed vacuum is generated in two temporal modes and one of these modes acts as an ancillary mode to make the other one a lar…
A superconducting qubit in the strong dispersive regime of a circuit quantum electrodynamics system is a powerful probe for microwave photons in a cavity mode. In this regime, a qubit spectrum is split into multiple peaks, with each peak corresponding to an individual photon number in the cavity (discrete ac Stark shift). Here, we measure the qubit spectrum in the cavity that is driven continuously with a squeezed vacuum field generated by a Josephson parametric amplifier. By fitting the qubit spectrum with a model which takes into account the finite qubit excitation power, the photon number d…
Nonclassical properties of photon added and photon subtracted squeezed coherent states have been compared with specific focus on the higher order nonclassicalities, such as higher order squeezing, higher order sub-Poissonian photon statistics, higher order antibunching. It is observed that both photon added and photon subtracted squeezed coherent states are highly nonclassical as they satisfy criteria for all of the above mentioned nonclassicalities and a set of other criteria including negativity of Wigner function, Klyshko's criterion and Agarwal's $(A_{3})$ parameter. Further, the amount of…
The quantum speed limit time for quantum system under squeezed environment is studied. We consider two typical models, the damped Jaynes-Cummings model and the dephasing model. For the damped Jaynes-Cummings model under squeezed environment, we find that the quantum speed limit time becomes larger with the squeezed parameter $r$ increasing and indicates symmetry about the phase parameter value $θ=π$. Meanwhile, the quantum speed limit time can also be influenced by the coupling strength between the system and environment. However, the quantum speed limit time for the dephasing model is determi…
Over the years, quite a few proposals have been put forward by various groups to exploit the Stern-Gerlach effect to create stable macroscopic spatial superpositions between micron-sized neutral test masses over appreciably long time scales. One such proposal put forward by Bose et al. and co-workers in 2017 uses this idea to show that two masses cannot be gravitationally entangled if not for the presence of a quantum coherent mediator. A key aspect of this approach involves the measure of the visibility of the SG-interferometer, a quantity that provides an estimate of the degree of spin coher…
Quasiclassical dynamics of trapped ions is characterized by applying the time dependent variational principle (TDVP) on coherent state orbits, in case of quadrupole and octupole combined (Paul and Penning) and radiofrequency (RF) traps. A dequantization algorithm is proposed, by which the classical Hamilton (energy) function associated to the system results as the expectation value of the quantum Hamiltonian on squeezed coherent states. We develop such method and particularize the quantum Hamiltonian for a combined and for a RF trap, with axial symmetry and a RF anharmonic electric potential. …
We first calculate the mean photon number and quadrature variance of superposed coherent and squeezed light, following a procedure of analysis based on combining the Hamiltonians and using the usual definition for the quadrature variance of superposed light beams. This procedure of analysis leads to physically unjustifiable mean photon number of the coherent light and quadrature variance of the superposed light. We then determine both of these properties employing a procedure of analysis based on superposing the Q functions and applying a slightly modified definition for the quadrature varianc…
We study the evolution of the hybrid entangled squeezed states of the qubit-oscillator system in the strong coupling domain. Following the adiabatic approximation we obtain the reduced density matrices of the qubit and the oscillator degrees of freedom. The oscillator reduced density matrix is utilized to calculate the quasiprobability distributions such as the Sudarshan-Glauber diagonal P -representation, the Wigner W -distribution, and the nonnegative Husimi Q-function. The negativity associated with the W -distribution acts as a measure of the nonclassicality of the state. The existence of …
A family of angular momentum coherent states on the sphere is constructed using previous work by Aragone et al [1]. These states depend on a complex parameter which allows an arbitrary squeezing of the angular momentum uncertainties. The time evolution of these states is analyzed assuming a rigid body hamiltonian. The rich scenario of fractional revivals is exhibited with cloning and many interference effects.
The the over-complete eigenvector system of the operator Q^{-1}P (Q:position, P:momentum) which consists of the squeezed states |0; s, t > with various s and t are investigated from the viewpoint of the annihilation and creation relations related to the algebra su(1,1). We derive a positive operator-valued measure(POVM) for the simultaneous measurement between the self-adjoint and anti-self-adjoint parts of PQ^{-1}.
