A heterostructure composed of two parallel homogeneous layers is studied in the limit as their widths $l_1$ and $l_2$, and the distance between them $r$ shrinks to zero simultaneously. The problem is investigated in one dimension and the squeezing potential in the Schrödinger equation is given by the strengths $V_1$ and $V_2$ depending on the layer thickness. A whole class of functions $V_1(l_1)$ and $V_2(l_2)$ is specified by certain limit characteristics as $l_1$ and $l_2$ tend to zero. The squeezing limit of the scattering data $a(k)$ and $b(k)$ derived for the finite system is shown to exist only if some conditions on the system parameters $V_j$, $l_j$, $j=1,2$, and $r$ take place. These conditions appear as a result of an appropriate cancellation of divergences. Two ways of this cancellation are carried out and the corresponding two resonance sets in the system parameter space are derived. On one of these sets, the existence of non-trivial bound states is proven in the squeezing limit, including the particular example of the squeezed potential in the form of the derivative of Dirac's delta function, contrary to the widespread opinion on the non-existence of bound states in $δ'$-like systems. The scenario how a single bound state survives in the squeezed system from a finite number of bound states in the finite system is described in detail.
A tunable double optomechanically induced transparency (OMIT) with a squeezed field is investigated in a system consisting of an optomechanical cavity coupled to a charged nanomechanical resonator via Coulomb interaction. Such a double OMIT can be achieved by adjusting the strength of the Coulomb interaction, and observed even with a single-photon squeezed field at finite temperature. Since it is robust against the cavity decay, but very sensitive to some parameters, such as the environmental temperature, the model under our consideration can be applied as a quantum thermometer for precision m…
This paper has been withdrawn. It is based on numerical results limited by computing resources to N=3000 atoms. Using a newly understood geometric method we find that the observed scaling with N saturates at around N=7000 or even higher. In light of this new finding we withdraw the paper and will submit a revised manuscript reflecting our new understanding.
A Mach-Zender interferometer with a gaussian number-difference squeezed input state can exhibit sub-shot-noise phase resolution over a large phase-interval. We obtain the optimal level of squeezing for a given phase-interval $Δθ_0$ and particle number $N$, with the resulting phase-estimation uncertainty smoothly approaching $3.5/N$ as $Δθ_0$ approaches 10/N, achieved with highly squeezed states near the Fock regime. We then analyze an adaptive measurement scheme which allows any phase on $(-π/2,π/2)$ to be measured with a precision of $3.5/N$ requiring only a few measurements, even for very la…
A novel two-mode non-degenerate squeezed light is generated based on a four-wave mixing (4WM) process driven by two pump fields crossing at a small angle. By exchanging the roles of the pump beams and the probe and conjugate beams, we have demonstrated the frequency-degenerate two-mode squeezed light with separated spatial patterns. Different from a 4WM process driven by one pump field, the refractive index of the corresponding probe field $n_{p}$ can be converted to a value that is greater than $1$ or less than $1$ by an angle adjustment. In the new region with $n_{p}<1$, the bandwidth of the…
We develop a theory of optomechanical cooling with a squeezed input light field. We show that Stokes heating transitions can be \emph{fully} suppressed when the driving field is squeezed below the vacuum noise level at an appropriately selected squeezing phase and for a finite amount of squeezing. The quantum backaction limit to laser cooling can be therefore moved down to zero and the resulting final temperature is then solely determined by the ratio between the thermal phonon number and the optomechanical cooperativity parameter, independently of the actual values of the cavity linewidth and…
We investigate the relative particle number squeezing produced in the excited states of a weakly interacting condensate at zero temperature by stimulated light scattering using a pair of lasers. We shall show that a modest number of relative number squeezed particles can be achieved when atoms with momentum $k$, produced in pairs through collisions in the condensate, are scattered out by their interaction with the lasers. This squeezing is optimal when the momentum $k$ is larger than the inverse healing length, $k>k_0$. This modest number of relative number squeezed particles has the potential…
The squeezed states of light become more and more important in the fields of quantum enhanced precision measurement and quantum information. To get this vital continuous variable quantum resource, the generation of squeezed states of light becomes a key factor. In this paper, a compact telecom fiber-based bright squeezed light (BSL) generator is demonstrated. To our knowledge, this is the first time that BSL has been reported in a fiber-based system to date. To obtain the BSL, a double-pass parametric amplifier based on surface-coated lithium niobate waveguide is employed. When the 1550 nm see…
We consider improving the sensitivity of future interferometric gravitational-wave detectors by simultaneously injecting two squeezed vacuums (light), filtered through a resonant Fabry-Perot cavity, into the dark port of the interferometer.The same scheme with single squeezed vacuum was first proposed and analyzed by Corbitt et al. Here we show that the extra squeezed vacuum, together with an additional homodyne detection suggested previously by one of the authors, allows reduction of quantum noise over the entire detection band. To motivate future implementations, we take into account a reali…
We propose to produce pulses of strongly squeezed light by Raman scattering of a strong laser pulse on a spin squeezed atomic sample. We prove that the emission is restricted to a single field mode which perfectly inherits the quantum correlations of the atomic system.
We develop a dissipative quantum state preparation scheme for the creation of phase- and number-squeezed states. It utilizes ultracold atoms in a double-well configuration immersed in a background Bose-Einstein condensate, with the latter consisting of an atom species different from the atoms in the double well and acting as a dissipative quantum reservoir. We derive a master equation for this system starting from microscopic physics, and show that squeezing develops on a time scale proportional to $1/N$, where $N$ is the number of particles in the double well. This scaling, caused by bosonic …
We present path integral ground state (PIGS) quantum Monte Carlo calculations for the ground state ($T = 0$) properties of repulsively interacting bosons in a three-dimensional external double well potential over a range of interaction strengths and potential parameters. We focus our calculations on ground state number statistics and the one-body density matrix in order to understand the level of squeezing and fragmentation that the system exhibits as a function of interaction strength. We compare our PIGS results to both a two-mode model and a recently-proposed eight-mode model. For weak inte…
Quantum pulsed second-subharmonic generation in a planar waveguide with a small periodic corrugation at the surface is studied. Back-scattering of the interacting fields on the corrugation enhances the nonlinear interaction giving larger values of squeezing. The problem of back-scattering is treated by perturbation theory, using the Fourier transform for non-dispersion propagation, and by numerical approach in the general case. Optimum spectral modes for squeezed-light generation are found using the Bloch-Messiah reduction. Improvement in squeezing and increase of numbers of generated photons …
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…
We report generation of a continuous-wave squeezed vacuum resonant on the Rb D_1 line (795 nm) using periodically poled KTiOPO_4 (PPKTP) crystals. With a frequency doubler and an optical parametric oscillator based on PPKTP crystals, we observed a squeezing level of -2.75 +- 0.14 dB and an anti-squeezing level of +7.00 +- 0.13 dB. This system could be utilized for demonstrating storage and retrieval of the squeezed vacuum, which is important for the ultra-precise measurement of atomic spins as well as quantum information processing.
We theoretically present the quantum Cramér-Rao bounds (QCRB) of an SU(1,1) interferometer for Gaussian states input with and without the internal photonic losses. The phase shifts in the single arm and in the double arms are studied and the corresponding analytical expressions of quantum Fisher information with Gaussian input states are presented. Different from the traditional Mach-Zehnder interferometer, the QCRB of single arm case is slightly higher or lower than that of double arms case depending on the input states. With a fixed mean photon number and for pure Gaussian state input, the o…
We modify the Araki-Woods double Fock space construction in order to describe general squeezed Gaussian states and use this to represent squeezed quantum stochastic noise processes. Associated master equations are derived.
The interference pattern in electron double-slit diffraction is a hallmark of quantum mechanics. A long standing question for stochastic electrodynamics (SED) is whether or not it is capable of reproducing such effects, as interference is a manifestation of quantum coherence. In this study, we use excited harmonic oscillators to directly test this quantum feature in SED. We use two counter-propagating dichromatic laser pulses to promote a ground-state harmonic oscillator to a squeezed Schrödinger cat state. Upon recombination of the two well-separated wavepackets, an interference pattern emerg…
As an "input" state of a linear (Mach-Zehnder or Ramsey) interferometer, the phase-squeezed state proposed by Berry and Wiseman exhibits the best sensitivity approaching to the Heisenberg limit [Phys. Rev. Lett. 85, 5098 (2000)]. In this paper, we find that it can be generated dynamically with atomic Bose-Einstein condensates confined in a symmetric double well. Similar with the Berry and Wiseman's state, the prepared states show the squeezing along spin operator S_y and the anti-squeezing along S_z, leading to a sub-shot-noise of the phase sensitivity.
We present a systematic study of the phenomena of number squeezing and fragmentation for a repulsive Bose-Einstein condensate (BEC) in a three dimensional double well potential over a range of interaction strengths and barrier heights, including geometries that exhibit appreciable overlap in the one-body wavefunctions localized in the left and right wells. We compute the properties of the condensate with numerically exact, full dimensional path integral ground state (PIGS) Quantum Monte Carlo simulations and compare with results obtained from using two- and eight-mode truncated basis models. T…
Dynamics of entangled states of two independent single-mode cavities in squeezed reservoirs is investigated in the context of matching of the correlations contained in the entangled states to those contained in the squeezed reservoir. We illustrate our considerations by examining the time evolution of entanglement of single and double excitation NOON and EPR states. A comparison is made when each cavity is coupled to own reservoir or both cavities are coupled to a common reservoir. It is shown that the evolution of the initial entanglement and transfer of entanglement from the squeezed reservo…
Strongly squeezed light finds many important applications within the fields of quantum metrology, quantum communication and quantum computation. However, due to the bulkiness and complexity of most squeezed light sources of today, they are still not a standard tool in quantum optics labs. We have taken the first steps in realizing a compact, high-performance 1550 nm squeezing source based on commercially available fiber components combined with a free-space double-resonant parametric down-conversion source. The whole setup, including single-pass second-harmonic generation in a waveguide, fits …
We analyze the formation of squeezed states in a condensate of ultracold bosonic atoms confined by a double-well potential. The emphasis is set on the dynamical formation of such states from initially coherent many-body quantum states. Two cases are described: the squeezing formation in the evolution of the system around the stable point, and in the short time evolution in the vicinity of an unstable point. The latter is shown to produce highly squeezed states on very short times. On the basis of a semiclassical approximation to the Bose-Hubbard Hamiltonian, we are able to predict the amount o…
We investigate the generation of photon-phonon entangled states by exploiting stimulated Brillouin scattering in nanoscale waveguides. The squeezing type Hamiltonian that represents creation and annihilation of photon-phonon pairs is obtained out of the multimode photon-phonon interaction Hamiltonian in the presence of a pump field. The Bogoliubov eigenstates of the Hamiltonian, which are a coherent mix of propagating photons and phonons, show squeezing properties in the uncertainties of the collective quadrature operators. The measurement of the photonic component can provide a controllable s…
After multiple scattering of quadrature-squeezed lights in a disordered medium, the quadrature amplitudes of the scattered modes present an excess noise above the shot-noise level [Opt. Expr. 14, 6919 (2006)]. A natural question is raised whether there exists a method of suppressing the quadrature fluctuation of the output mode. The answer is affirmative. In this work, we prove that wavefront shaping is a promising method to reduce the quantum noise of quadrature amplitudes of the scattered modes. This reduction is owing to the destructive interference of quantum noise. Specifically, when the …
We present an entanglement criterion for two mode squeezed states which relies on particle counting only. The proposed inequality is optimal for the state under consideration and robust against particle losses up to 2/3. As it does not involve measurements of quadratures - which is typically very challenging for atomic modes - it renders the detection of atomic many-particle entanglement feasible in many different settings. Moreover it bridges the gap between entanglement verification for a qubit and criteria for continuous variables measured by homodyne detection. We illustrate its applicatio…
We study the properties of bi-squeezed tripartite Gaussian states created by two spontaneous parametric down-conversion processes that share a common idler. We give a complete description of the quantum correlations across of all partitions, as well as of the genuine multipartite entanglement, obtaining analytical expressions for most of the quantities of interest. We find that the state contains genuine tripartite entanglement, in addition to the bipartite entanglement among the modes that are directly squeezed. We also investigate the effect of homodyne detection of the photons in the common…
Squeezed states of light have found their way into a number of applications in quantum-enhanced metrology due to their reduced noise properties. In order to extend such an enhancement to metrology experiments based on atomic ensembles, an efficient light-atom interaction is required. Thus, there is a particular interest in generating narrow-band squeezed light that is on atomic resonance. This will make it possible not only to enhance the sensitivity of atomic based sensors, but also to deterministically entangle two distant atomic ensembles. We generate bright two-mode squeezed states of ligh…
Scattering discussion due to Double Dirac Equation in Quaternionic version of relativistic quantum mechanics has been studied in this paper in details. In such a quantum mechanics Dirac equation in presence vector and scalar potential has been considered. Then a Quaternionic double Dirac delta potential comes to our considered system which causes to scatter the particles. Scattering states of the particles have been derived as well as reflected and transmission coefficients are calculated.
We discuss how two-photon absorption (TPA) of squeezed and coherent states of light can be detected in measurements of the transmitted light fields. Such measurements typically suffer from competing loss mechanisms such as experimental imperfections and linear scattering losses inside the sample itself, which can lead to incorrect assessments of the two-photon absorption cross section. We evaluate the sensitivity with which TPA can be detected and find that TPA sensitivity of squeezed vacua or squeezed coherent states can become independent of linear losses at sufficiently large photon numbers…
In this paper, we investigate theoretically a system consisting of a one dimensional Bose-Einstein condensate trapped inside the optical lattice of an optical cavity. In the weak-interaction regime and under the Bogoliubov approximation, the wave function of the Bose-Einstein condensate can be described by a classical field (condensate mode) having some quantum fluctuations (the Bogoliubov mode) about the mean value. Such a system behaves as a so-called atomic parametric amplifier, similar to an optical parametric amplifier, where the condensate and the Bogoliubov modes play respectively, the …
We theoretically investigate the creation of squeezed states of a Bose-Einstein Condensate (BEC) trapped in a magnetic double well potential. The number or phase squeezed states are created by modulating the tunnel coupling between the two wells periodically with twice the Josephson frequency, i.e., through parametric amplification. Simulations are performed with the multi configurational Hartree method for bosons (MCTDHB). We employ optimal control theory to bring the condensate to a complete halt at a final time, thus creating a highly squeezed state (squeezing factor of 0.12, $ξ_S^2=-18$ dB…
We describe a six-parameter family of the minimum-uncertainty squeezed states for the harmonic oscillator in nonrelativistic quantum mechanics. They are derived by the action of corresponding maximal kinematical invariance group on the standard ground state solution. We show that the product of the variances attains the required minimum value 1/4 only at the instances that one variance is a minimum and the other is a maximum, when the squeezing of one of the variances occurs. The generalized coherent states are explicitly constructed and their Wigner function is studied. The overlap coefficien…
We study the sensitivity of phase estimation in a lossy Mach-Zehnder interferometer (MZI) using two general, and practical, resources generated by a laser and a nonlinear optical medium with passive optimal elements, which are readily available in the laboratory: One is a two-mode separable coherent and squeezed vacuum state at a beam splitter and the other is a two-mode squeezed vacuum state. In view of the ultimate precision given by quantum Fisher information, we show that the two-mode squeezed vacuum state can achieve a lower bound of estimation error than the coherent and squeezed vacuum …
We examine how to signify and quantify the mesoscopic quantum coherence of approximate two-mode NOON states and spin-squeezed two-mode Bose-Einstein condensates (BEC). We identify two criteria that verify a nonzero quantum coherence between states with quantum number different by $n$. These criteria negate certain mixtures of quantum states, thereby signifying a generalised $n$-scopic Schrodinger cat-type paradox. The first criterion is the correlation $\langle\hat{a}^{\dagger n}\hat{b}^{n}\rangle\neq0$ (here $\hat{a}$ and $\hat{b}$ are the boson operators for each mode). The correlation manif…
We analyse the entanglement generation in a one dimensional scattering process. The two colliding particles have a Gaussian wave function and interact by hard--core repulsion.In our analysis results on the entanglement of two mode Gaussian states are used. The produced entanglement depends in a non-obvious way on the parameters ratio of masses and initial widths. The asymptotic wavefunction of the two particles and its associated ellipse yield additional geometric insight into these conditions. The difference to the quantitative analysis of the amount of entanglement generated by beam splitter…
We study the inelastic scattering of a probe particle on a Bose-Einstein condensate confined in a double-well potential. We identify prominent signatures of the underlying mean-field phase space in the scattering signal and derive an analytical expression for the inelastic scattering cross section.
