Optimal Squeezing Research Articles

Preparing entangled states of two atoms through the intensity-dependent interaction with the two-mode squeezed vacuum

Two four-level atoms resonantly interacting with a two-mode squeezed vacuum field through the intensity-dependent Jaynes–Cummings-like model are considered. It is shown that the atoms can evolve into pure entangled states at certain time. Moreover, the pure entangled states can probabilistically be projected onto extremely entangled states by quantum jump technique. It is shown that the success probability monotonously increases with increasing degree of squeezing without any decoherence processes. However, it is found that if decoherence processes such as atomic spontaneous emission and photon leakage out of the cavity take place, the total success probability first increases but then decreases with increasing degree of squeezing and finally approaches zero as the squeezing becomes stronger and stronger. Therefore, the high degree of squeezing in the initial state of the cavity field is not always helpful for a high probability of creating extremely entangled states when spontaneous emission and cavity decay exist. Given spontaneous emission and photon leakage rates, there is an optimal squeezing degree for which the total success probability becomes maximum.

Optimal Squeezing and Entanglement from Noisy Gaussian Operations

We investigate the creation of squeezing via operations subject to noise and losses and ask for the optimal use of such devices when supplemented by noiseless passive operations. Both single and repeated uses of the device are optimized analytically and it is proven that in the latter case the squeezing converges exponentially fast to its asymptotic optimum, which we determine explicitly. For the case of multiple iterations we show that the optimum can be achieved with fixed intermediate passive operations. Finally, we relate the results to the generation of entanglement and derive the maximal two-mode entanglement achievable within the considered scenario.

Atom nanolithography with multilayer light masks: Particle optics analysis

We study the focusing of atoms by multiple layers of standing light waves in the context of atom lithography. In particular, atomic localization by a double-layer light mask is examined using the optimal squeezing approach. Operation of the focusing setup is analyzed both in the paraxial approximation and in the regime of nonlinear spatial squeezing for the thin-thin as well as thin-thick atom lens combinations. It is shown that the optimized double light mask may considerably reduce the imaging problems, improve the quality of focusing and enhance the contrast ratio of the deposited structures.

Quantum theory of fibre Bragg grating solitons

Following the pioneering work of Professor Haus, a general quantum theory for bi-directional nonlinear optical pulse propagation problems is developed and applied to study the quantum properties of fibre Bragg grating solitons. Fibre Bragg grating solitons are found to be automatically amplitude squeezed after passing through the grating and the squeezing ratio saturates after a certain grating length. The optimal squeezing ratio occurs when the pulse energy is slightly above the fundamental soliton energy. One can also compress the soliton pulsewidth and enhance the squeezing simultaneously by using an apodized grating, as long as the solitons evolve adiabatically.

Quantum fluctuations around bistable solitons in the cubic–quintic nonlinear Schrödinger equation

Small quantum fluctuations in solitons described by the cubic–quintic nonlinear Schrodinger equation (CQNLSE) are studied within the linear approximation. The cases of both self-defocusing and self-focusing quintic terms are considered (in the latter case, the solitons may be effectively stable, despite the possibility of collapse). The numerically implemented back-propagation method is used to calculate the optimal squeezing ratio for the quantum fluctuations versus the propagation distance. In the case of self-defocusing quintic nonlinearity, opposite signs in front of the cubic and quintic terms make the fluctuations around bistable pairs of solitons (which have different energies for the same width) totally different. The fluctuations of nonstationary Gaussian pulses in the CQNLSE model are also studied.

EIT-assisted atomic squeezing

The interaction of classical and quantized electromagnetic fields with an ensemble of atoms in an optical cavity is considered. Four fields drive a double-Λ level scheme in the atoms, consisting of a pair of Λ systems sharing the same set of lower levels. Two of the fields produce maximum coherence, ρ12 ≈− 1/2, between the ground state sublevels 1 and 2. This pumping scheme involves equal intensity fields that are resonant with both the one- and two-photon transitions of the Λ system. There is no steady-state absorption of these fields, implying that the fields induce a type Electromagnetically-Induced Transparency (EIT) in the medium. An additional pair of fields interacting with the second Λ system, combined with the EIT fields, leads to squeezing of the atom spin associated with the ground state sublevels. Our method involves a new mechanism for creating steady-state spin squeezing using an optical cavity. As the cooperativity parameter C is increased, the optimal squeezing varies as C −1/3 . For experimentally accessible values of C, squeezing as large as 90% can be achieved.

Squeezed-input, optical-spring, signal-recycled gravitational-wave detectors

We theoretically analyze the quantum noise of signal-recycled laser interferometric gravitational-wave detectors with additional input and output optics, namely frequency-dependent squeezing of the vacuum entering the dark port and frequency-dependent homodyne detection. We combine the work of Buonanno and Chen on the quantum noise of signal-recycled interferometers with ordinary input-output optics, and the work of Kimble el al. on frequency-dependent input-output optics with conventional interferometers. Analytical formulas for the optimal input and output frequency dependencies are obtained. It is shown that injecting squeezed light with the optimal frequency-dependent squeezing angle into the dark port yields an improvement on the noise spectral density by a factor of exp(-2r) (in power) over the entire squeezing bandwidth, where r is the squeezing parameter. It is further shown that frequency-dependent (variational) homodyne read-out leads to an additional increase in sensitivity which is significant in the wings of the doubly resonant structure. The optimal variational input squeezing in case of an ordinary output homodyne detection is shown to be realizable by applying two optical filters on a frequency-independent squeezed vacuum. Throughout this paper, we take as example the signal-recycled topology currently being completed at the GEO600 site. However, theoretical results obtained here are also applicable to the proposed topology of Advanced LIGO.

Squeezing effect in a driven coupled-oscillator system: A dual role of damping

We investigate in detail the role of a reservoir concerning the squeezing effect in a driven coupled-oscillator system. In our model, a harmonic oscillator (single cavity mode) is coupled to a two-state oscillator (two-level atom) driven by a classical field. The oscillators are coupled to their respective reservoirs, by which the oscillators are damped. The degree of squeezing in the short-time limit is found to be independent of the damping rate of the harmonic oscillator in a perturbative regime. More remarkably, the harmonic oscillator, which is in a coherent state in the absence of its reservoir, gets squeezed in the steady state when it is coupled to the reservoir. The reservoir assumes two competing roles of assisting and suppressing the squeezing effect induced by the nonlinear interaction of the coupled oscillators. As a result, the squeezing effect is increased to some extent with the damping rate of the harmonic oscillator. In addition, the ``matching condition'' for the optimal squeezing is obtained such that the pumping field intensity should be inversely proportional to the damping rate.

Quantum state transfer from light beams to atomic ensembles

We show the equivalence between an ensemble of two-level atoms driven by a squeezed vacuum field, and a harmonic oscillator coupled to a squeezed field. We give the conditions for optimal squeezing transfer from the field to the atomic ensemble. We show that EPR-type correlations are created between the atomic ensemble and the incoming field.

Optimal squeezing, pure states, and amplification of squeezing in resonance fluorescence

It is shown that 100% squeezed output can be produced in the resonance fluorescence from a coherently driven two-level atom interacting with a squeezed vacuum. This is only possible for $N=1/8$ squeezed input, and is associated with a pure atomic state, i.e., a completely polarized state. The quadrature for which optimal squeezing occurs depends on the squeezing phase $\Phi ,$ the Rabi frequency $\Omega ,$ and the atomic detuning $\Delta $. Pure states are described for arbitrary $\Phi ,$ not just $\Phi =0$ or $\pi $ as in previous work. For small values of $N,$ there may be a greater degree of squeezing in the output field than the input - i.e., we have squeezing amplification.

Control of quantized photon states with cascade phase conjugators by modulation pumping

Squeezing properties of a quantized photon field interacting with cascade four-wave-mixing materials (phase conjugators) are investigated theoretically by the transfer-matrix method. The controllability of the quantum fluctuation of the photon field is improved with the use of modulation pumping, in which phases of pumping beams of the phase conjugators are individually controlled even when their optical nonlinearity and/or the pumping power are fixed. By choosing appropriate numbers of phase conjugators and phase differences of the pump beams, incident coherent light is transformed to quadrature-phase-amplitude (QPA) squeezed states and photon-number-squeezed states. Optimal squeezing of both the QPA and photon number can be realized with this cascade system by modulation pumping. Partial (normal) reflection of light at surfaces of the phase conjugators is shown quantitatively to suppress the squeezing. Comparison with an ordinary method using a single-phase conjugator is also made.

Generation of higher-order squeezing in a micromaser

The fourth-order squeezing and amplitude-squared squeezing of cotangent states produced in one-atom micromasers are investigated. It is found that optimal squeezing in the cotangent state can be achieved by properly choosing the relative amplitudes of the atomic coherent state. From our study of the dynamic process of the generation of steady-state fourth-order squeezing and amplitude-squared squeezing in one-atom micromasers, it is also shown that for sufficiently large atomic flux, the cavity loss, and finite temperature in the cavity have very little influence on the generation of these higher-order squeezings in practice.

Feedback-enhanced squeezing in second-harmonic generation.

Second-harmonic generation, in a cavity resonant only at the fundamental, produces amplitude squeezing in both the fundamental and the second harmonic, with optimal squeezing of -1/3 and -8/9, respectively, at low frequency. It also produces nonclassical correlations between the two output beams. We show that these correlations can be used to enhance the squeezing in either beam by constructing a feedback loop. By using the second-harmonic photocurrent to control the amplitude of the pump, the optimal fundamental squeezing is enhanced by 50% to -1/2. The limit of -8/9 for the seocnd harmonic (for infinite nonlinearity strength) cannot be improved by feeding back the fundamental. However, for any fixed finite nonlinearity, such feedback can produce significant enhancement, with a maximum of 50%. Even with the losses characteristic of a practical experiment included, the enchancement offered by the feedback is still significant, being greater than 20% in either mode.

Optimal squeezing of vibrational wave packets in sodium dimers

We present an application of ‘‘optimal squeezing’’ theory to the design of laser pulses for generation of squeezed states of material waves (states whose localization in some variable exceeds that of the ground state) in Na2. Spatiotemporal evolution of the squeezed states during and after the laser pulse is studied. We show that the optimized laser pulses can affect squeezing via three basic scenarios whose realizations depend on the desired position of the wave packet and target squeezing times. These scenarios are alternations between momentum-space and coordinate-space squeezing, interfering collisions between wave packets, and overtaking of a slow front by a fast tail.

Squeezed-light generation by twin-beam control with an optical cavity.

We demonstrate that a single-ended optical cavity can be used to generate squeezed light from a pair of intensity-correlated light beams. One beam serves as an input to the cavity, while the measured intensity in the other beam serves to control various cavity parameters such as input coupling, losses, or detuning. Depending on the mode of operation, the resulting output beam from the cavity can be squeezed in amplitude or in phase. We derive the noise spectrum for the case of optimal amplitude squeezing, provided that there are no initial correlations between amplitude and phase in the input beams. Practical examples are given in which an optical parametric oscillator serves as the twin-beam source. As a general consequence of twin-beam control, we also derive a Heisenberg-like inequality governing the amplitude and phase spectra of intensity-correlated beams.

The effect of loss asymmetry on the nonclassical properties of nondegenerate parametric devices

The effect of linear absoption loss asymmetry on two-mode squeezing in nondegenerate parametric oscillation and amplification is analysed. The interbeam correlations show time-displaced maxima, which we have analytically identified. The analysis of the intensity difference fluctuations shows that the essential factor governing noise reduction is the proper balancing of the system which, in some cases, may be enhanced by increasing the total losses. Finally, an interesting interplay between loss asymmetry and twin beam frequency splitting arises in the analysis of two-mode quadrature squeezing by means of heterodyne detection. Though no perfect squeezing is possible, we have identified optimal squeezing parameter regions and local minima.

Optimal squeezing of molecular wave packets.

We present a practical method of designing laser fields for generation of spatially squeezed molecular wave packets. Our approach, based on optimal control theory, generalizes and improves previous, more intuitive suggestions for the optical generation of squeezed wave packets. Spatial-temporal evolution of the squeezing is studied and several underlying physical mechanisms of the effect are explored. Possible applications to laser femtosecond chemistry and experiments on laser modification of molecular adiabatic potentials are discussed.

Single-beam squeezed-state generation in sodium vapor and its self-focusing limitations

We describe an experiment that generates squeezed states by means of forward four-wave mixing in sodium vapor with a single optical beam. The single-beam arrangement maximizes the pump-probe spatial overlap in the nonlinear medium. Self-focusing (or self-defocusing) is found to be the major limiting factor in achieving optimal squeezing.

Limits on quadrature variances and cross-correlations

An arbitrary radiation field has limits on its quadrature variances and cross-correlations given by the positivity of the density matrix. These limits are derived and related to the optimisation of the squeezing measurements. The results are designed to deal with typical multimode squeezing experiments. In particular, the bounds indicate the necessity of achieving equal photon number intensities for optimal squeezing. A photon number imbalance can be compensated to some extent by using unequal gains. The optimal relative gain is obtained here.

Time dependence of quantum fluctuations in solitons

We investigate quantum fluctuations in coherent solitons propagating in a dispersive nonlinear waveguide. Optimal squeezing or noise reduction occurs for a local oscillator width near the soliton width in time, i.e., the quantum fluctuations are localized.