Gravitational well is a widely used system for the verification of the quantum weak equivalence principle (WEP). We have studied the quantum gravitational well (GW) under the shed of noncommutative (NC) space so that the results can be utilized for testing the validity of WEP in NC-space. To keep our study widely usable, we have considered both position-position and momentum-momentum noncommutativity.
Since coherent state (CS) structure provides a natural bridging between the classical and quantum domain descriptions, the quantum domain validity of purely classical phenomena like free-fall under gravity might be verified with the help of CS. We have constructed CS with the aid of a Lewis-Riesenfeld phase space invariant operator. From the uncertainty relations deduced from the expectation values of the observables, we have shown that the solutions of the time-dependent Schrödinger equation are squeezed-coherent states.
One examines putative corrections to the Bell operator due to the noncommutativity in the phase-space. Starting from a Gaussian squeezed envelop whose time evolution is driven by commutative (standard quantum mechanics) and noncommutative dynamics respectively, one concludes that, although the time evolving covariance matrix in the noncommutative case is different from the standard case, the squeezing parameter dominates and there are no noticeable noncommutative corrections to the Bell operator. This indicates that, at least for squeezed states, the privileged states to test Bell correlations…
We provide an explicit construction of entangled states in a noncommutative space with nonclassical states, particularly with the squeezed states. Noncommutative systems are found to be more entangled than the usual quantum mechanical systems. The noncommutative parameter provides an additional degree of freedom in the construction by which one can raise the entanglement of the noncommutative systems to fairly higher values beyond the usual systems. Despite of having classical-like behaviour, coherent states in noncommutative space produce little amount of entanglement and therefore they posse…
As an application of the simultaneous and continuous measurement of noncommutative observables formulated in our previous paper [C. Jiang and G. Watanabe, Phys. Rev. A 102, 062216 (2020)], we propose a scheme to generate the pure ideal quadrature-squeezed state in a one-dimensional harmonic oscillator system by the feedback control based on such type of measurement of noncommutative quadrature observables. We find that, by appropriately setting the strengths of the measurement and the feedback control, the pure ideal quadrature-squeezed state with arbitrary squeezedness can be produced. This i…
We provide an explicit construction for Gazeau-Klauder coherent states related to non-Hermitian Hamiltonians with discrete bounded below and nondegenerate eigenspectrum. The underlying spacetime structure is taken to be of a noncommutative type with associated uncertainty relations implying minimal lengths. The uncertainty relations for the constructed states are shown to be saturated in a Hermitian as well as a non-Hermitian setting for a perturbed harmonic oscillator. The computed value of the Mandel parameter dictates that the coherent wavepackets are assembled according to sub-Poissonian s…
We study several classical like properties of q-deformed nonlinear coherent states as well as nonclassical behaviours of q-deformed version of the Schrodinger cat states in noncommutative space. Coherent states in q-deformed space are found to be minimum uncertainty states together with the squeezed photon distributions unlike the ordinary systems, where the photon distributions are always Poissonian. Several advantages of utilising cat states in noncommutative space over the standard quantum mechanical spaces have been reported here. For instance, the q-deformed parameter has been utilised to…
We study the harvesting of entanglement and mutual information by Unruh-DeWitt particle detectors from thermal and squeezed coherent field states. We prove (for arbitrary spatial dimensions, switching profiles and detector smearings) that while the entanglement harvesting ability of detectors decreases monotonically with the field temperature $T$, harvested mutual information grows linearly with $T$. We also show that entanglement harvesting from a general squeezed coherent state is independent of the coherent amplitude, but depends strongly on the squeezing amplitude. Moreover, we find that h…
In a setting of noncommutative space with minimal length we confirm the general assertion that the more nonclassical an input state for a beam splitter is, the more entangled its output state becomes. By analysing various nonclassical properties we find that the odd Schrödinger cat states are more nonclassical than the even Schrödinger cat states, hence producing more entanglement, which in turn are more nonclassical than coherent states. Both the nonclassicality and the entanglement can be enhanced by increasing the noncommutativity of the underlying space. In addition we find as a by-product…
The Generalized Uncertainty Principle (GUP) is a modification of Heisenberg's Principle predicted by several theories of Quantum Gravity. It consists of a modified commutator between position and momentum. In this work we compute potentially observable effects that GUP implies for the harmonic oscillator, coherent and squeezed states in Quantum Mechanics. In particular, we rigorously analyze the GUP-perturbed harmonic oscillator Hamiltonian, defining new operators that act as ladder operators on the perturbed states. We use these operators to define the new coherent and squeezed states. We com…
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.
In two-dimensional space a subtle point that for the case of both space-space and momentum-momentum noncommuting, different from the case of only space-space noncommuting, the deformed Heisenberg-Weyl algebra in noncommutative space is not completely equivalent to the undeformed Heisenberg-Weyl algebra in commutative space is clarified. It follows that there is no well defined procedure to construct the deformed position-position coherent state or the deformed momentum-momentum coherent state from the undeformed position-momentum coherent state. Identifications of the deformed position-positio…
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.
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 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.
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.
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.
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…
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…
Entangled coherent states are shown to emerge, with high fidelity, when mixing coherent and squeezed vacuum states of light on a beam-splitter. These maximally entangled states, where photons bunch at the exit of a beamsplitter, are measured experimentally by Fock-state projections. Entanglement is examined theoretically using a Bell-type nonlocality test and compared with ideal entangled coherent states. We experimentally show nearly perfect similarity with entangled coherent states for an optimal ratio of coherent and squeezed vacuum light. In our scheme, entangled coherent states are genera…
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 develop a systematic variational coherent-squeezed-state expansion for the ground state of the quantum Rabi model, which includes an additional squeezing effect with comparisons to previous coherent-state approach. For finite large ratio between the atomic and field frequency, the essential feature of the ground-state wave function in the super-radiant phase appears, which has a structure of two delocalized wake packets. The single-peaked wave function with one coherent-squeezed state works well even around the critical regime, exhibiting the advantage over the coherent-state method. As the…
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.
We report the experimental demonstration of coherent control with high power, broadband squeezed vacuum. Although incoherent and exhibiting the statistics of a thermal noise, broadband squeezed vacuum is shown to induce certain two-photon interactions as a coherent ultrashort pulse with the same spectral bandwidth. Utilizing pulse-shaping techniques we coherently control the sum-frequency generation of broadband squeezed vacuum over a range of two orders of magnitude. Coherent control of two-photon interactions with broadband squeezed vacuum can potentially obtain spectral resolutions and exti…
Conditions to generate high-purity entangled vacuum-evacuated coherent states ($|0>|α>^0 - |-α>^0 |0>$ were studied for two cascade-placed beam splitters, with one squeezed state input and two coherent state inputs whenever a single photon is detected. Controlling the amplitudes and the phases of the beams allows for various amplitudes of the vacuum-evacuated coherent states ($|α>^ 0 = |α> -e^{-|α|^2} |0> $) up to $α= 2.160$ to be manipulated with high-purity.
In this parer, q-deformed oscillator for pseudo-Hermitian systems is investigated and pseudo-Hermitian appropriate coherent and squeezed states are studied. Also, some basic properties of these states is surveyed. The over-completeness property of the para-Grassmannian pseudo-Hermitian coherent states (PGPHCSs) examined, and also the stability of coherent and squeezed states discussed. The pseudo-Hermitian supercoherent states as the product of a pseudo-Hermitian bosonic coherent state and a para-Grassmannian pseudo-Hermitian coherent state introduced, and the method also developed to define p…
We determine the Rabi oscillations for coherent and squeezed coherent states via one- and two-photon atomic transitions in two- and three-level atoms, respectively. The effect of squeezing coherent states is to reduce the large number of photons of mesoscopic scale to fewer photons and so be able to use numerical solutions with the aid of the Jaynes-Cummings model. We maximize the squeezing of the coherent state by minimizing the ratio of the photon number variance to photon number, thus narrowing the region where revival occurs.
We explore squeezed coherent states of a 3-dimensional generalized isotonic oscillator whose radial part is the newly introduced generalized isotonic oscillator whose bound state solutions have been shown to admit the recently discovered $X_1$-Laguerre polynomials. We construct a complete set of squeezed coherent states of this oscillator by exploring the squeezed coherent states of the radial part and combining the latter with the squeezed coherent states of the angular part. We also prove that the three mode squeezed coherent states resolve the identity operator. We evaluate Mandel's $Q$-par…
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 …
Phase-squeezed light can enhance the precision of optical phase estimation. The larger the photon numbers are and the stronger the squeezing is, the better the precision will be. We propose an experimental scheme for generating phase-squeezed light pulses with large coherent amplitudes. In our scheme, one arm of a single-photon Mach-Zehnder interferometer interacts with coherent light via a non-linear optical Kerr medium to generate a coherent superposition state. Post-selecting the single photon by properly tuning a variable beam splitter in the interferometer yields a phase-squeezed output.
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…
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 w…
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…
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…
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…
With the successes of the Laser Interferometer Gravitational-wave Observatory, we anticipate increased interest in working with squeezed states in the undergraduate and graduate quantum-mechanics classroom. Because squeezed-coherent states are minimum uncertainty states, their wavefunctions in position and momentum space must be Gaussians. But this result is rarely discussed in treatments of squeezed states in quantum textbooks or quantum optics textbooks. In this work, we show three different ways to construct the wavefunction for squeezed-coherent states: (i) a differential equation-based ap…
We investigate coherent perfect absorption (CPA) in quantum optics, in particular when pairs of squeezed coherent states of light are superposed on an absorbing beam splitter. First, by employing quantum optical input-output relations, we derive the absorption coefficients for quantum coherence and for intensity, and reveal how these will differ for squeezed states. Secondly, we present the remarkable properties of a CPA-gate: two identical but otherwise arbitrary incoming squeezed coherent states can be completely stripped off their coherence, producing a pure entangled squeezed vacuum state …
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…
Coherent and squeezed phonon oscillations can be excited in solids impulsively by a single femtosecond pulse whose duration is shorter that a phonon period. By applying the second ultrafast pump pulse these oscillations can be significantly, but differently modified.
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}.
