Octavio Castanos, Ramon Lopez-Pena, Margarita A. Man'ko, Vladimir I. Man'ko
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17 pages LaTeX, 2 figures PostScript To appear in the Proccedings of the Conference ``Topics in Mathematical Physics, General Relativity and Cosmology on the Ocassion of the 75th Birthday of Professor Jerzy F. Plebanski'' Mexico City, August 2002 (World Scientific, Singapore)
Some properties of Plebanski squeezing operator and squeezed states created with time-dependent quadratic in position and momentum Hamiltonians are reviewed. New type of tomography of quantum states called squeeze tomography is discussed.
We find that the exponential operator V=exp[ilamda (Q_1P_2+Q_2P_3+...+Q_{n-1}P_{n}+Q_{n}P_1)], Q_{i}, P_{i} are respectively the coordinate and momentum operators, is an n-mode squeezing operator which engenders standard squeezing. By virtue of the technique of integration within an ordered product of operators we derive V's normally ordered expansion and obtain the n-mode squeezed vacuum states, its Wigner function is calculated by using the Weyl ordering invariance under similar transformations.
We propose an efficient approach to generate the superposed macroscopically squeezed states with enhanced squeezing in a two-mode optomechanical system. This can be achieved by introducing a sinusoidal modulation to either the cavity frequencies or the coupling strengths between two cavity modes. The squeezement of the oscillator can be significantly enhanced to 12.16 dB with single photon, once the relative ratio of coupling strength is optimized under proper conditions. Further enhanced squeezing can be obtained by carefully adjusting the system parameters. In terms of the Wigner quasi-proba…
In this paper, we theoretically investigate the displacement and momentum fluctuations spectra of the movable mirror in a standard optomechanical system driven by a finite bandwidth squeezed vacuum light accompanying a coherent laser field. Two cases in which the squeezed vacuum is generated by degenerated and non-degenerate parametric oscillators (DPO and NDPO) are considered. We find that for the case of finite bandwidth squeezed vacuum injection, the two spectra exhibit unique features, which strongly differ from those of broadband squeezing excitation. In particular, the spectra exhibit a …
We propose a scheme to generate entanglement between two cavity modes and squeeze magnon mode in a magnon-cavity QED system, where the two microwave cavity modes are coupled with a massive yttrium iron garnet (YIG) sphere through magnetic dipole interaction. The nonlinearity used in our system originates from a squeezed driving via parametric down-conversion process, which is the reason to cause entanglement and squeezing. By using the mean field approximation and employing experimentally feasible parameters, we demonstrate that the system shows zero entanglement and squeezing without squeezed…
We propose a scheme to generate strong and robust mechanical squeezing in an optomechanical system in the highly unresolved sideband (HURSB) regime with the help of the Duffing nonlinearity and intracavity squeezed light. The system is formed by a standard optomechanical system with the Duffing nonlinearity (mechanical nonlinearity) and a second-order nonlinear medium (optical nonlinearity). In the resolved sideband regime, the second-order nonlinear medium may play a destructive role in the generation of mechanical squeezing. However, it can significantly increase the mechanical squeezing (la…
We consider the thermodynamic properties of the squeezed vacuum state of a frequency--modulated quantum harmonic oscillator. We analytically relate the squeezing parameter to the irreversible work and the degree of nonadiabaticity of the frequency transformation. We furthermore determine the optimal modulation that leads to maximal squeezing, and discuss its implementation as well as the detection of squeezing in single cold ion traps.
It is known that exp[i\lamda(Q_1P_1-i/2)] is a unitary single-mode squeezing operator, where Q_1,P_1 are the coordinate and momentum operators, respectively. In this paper we employ Dirac's coordinate representation to prove that the exponential operator S_{n}=Exp[i\lamda sum_{i=1}^{n}](Q_{i}P_{i+1}+Q_{i+1}P_{i}))], (Q_{n+1}=Q_1P_{n+1}=P_1), is a n-mode squeezing operator which enhances the standard squeezing. By virtue of the technique of integration within an ordered product of operators we derive S_{n}'s normally ordered expansion and obtain new n-mode squeezed vacuum states, its Wigner fun…
Electro-optical feedback can produce an in-loop photocurrent with arbitrarily low noise. This is not regarded as evidence of `real' squeezing because squeezed light cannot be extracted from the loop using a linear beam splitter. Here I show that illuminating an atom (which is a nonlinear optical element) with `in-loop' squeezed light causes line-narrowing of one quadrature of the atom's fluorescence. This has long been regarded as an effect which can only be produced by squeezing. Experiments on atoms using in-loop squeezing should be much easier than those with conventional sources of squeeze…
A general analysis of squeezing transformations for two mode systems is given based on the four dimensional real symplectic group $Sp(4,\Re)\/$. Within the framework of the unitary metaplectic representation of this group, a distinction between compact photon number conserving and noncompact photon number nonconserving squeezing transformations is made. We exploit the $Sp(4,\Re)-SO(3,2)\/$ local isomorphism and the $U(2)\/$ invariant squeezing criterion to divide the set of all squeezing transformations into a two parameter family of distinct equivalence classes with representative elements ch…
We analyze the spectral properties of squeezed light produced by means of pulsed, single-pass degenerate parametric down-conversion. The multimode output of this process can be decomposed into characteristic modes undergoing independent squeezing evolution akin to the Schmidt decomposition of the biphoton spectrum. The main features of this decomposition can be understood using a simple analytical model developed in the perturbative regime. In the strong pumping regime, for which the perturbative approach is not valid, we present a numerical analysis, specializing to the case of one-dimensiona…
By extending the usual two-mode squeezing operator $S_{2}=\exp [ iλ(Q_{1}P_{2}+Q_{2}P_{1}) ] $ to the three-mode squeezing operator $S_{3}=\exp {iλ[ Q_{1}(P_{2}+P_{3}) +Q_{2}(P_{1}+P_{3}) +Q_{3}(P_{1}+P_{2}) ]} $, we obtain the corresponding three-mode squeezed coherent state. The state's higher-order properties, such as higher-order squeezing and higher-order sub-Possonian photon statistics, are investigated. It is found that the new squeezed state not only can be squeezed to all even orders but also exhibits squeezing enhancement comparing with the usual cases. In addition, we examine the vi…
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 $Φ,$ the Rabi frequency $Ω,$ and the atomic detuning $Δ$. Pure states are described for arbitrary $Φ,$ not just $Φ=0$ or $π$ as in previous work. For small values of $N,$ there may be a greater degree of squeezing in the output f…
It was shown by a study of the incoherent part of the low-frequency resonance fluorescence spectrum of the polar quantum emitter driven by semiclassical external laser field and damped by non-squeezed vacuum reservoir that the emitted fluorescence field is squeezed to some degree nevertheless. As was also found, a higher degree of squeezing could, in principle, be achieved by damping the emitter by squeezed vacuum reservoir.
We propose a scheme for quantum cryptography that uses the squeezing phase of a two-mode squeezed state to transmit information securely between two parties. The basic principle behind this scheme is the fact that each mode of the squeezed field by itself does not contain any information regarding the squeezing phase. The squeezing phase can only be obtained through a joint measurement of the two modes. This, combined with the fact that it is possible to perform remote squeezing measurements, makes it possible to implement a secure quantum communication scheme in which a deterministic signal c…
In a 3-wave mixing process occurring in some nonlinear optical medium when }$a_{1}^{\dagger}${\small mode interacts with both }$a_{2}^{\dagger}% ${\small mode and }$a_{3}^{\dagger}${\small mode, we theoretically study the squeezing effect generated by the operator }$S_{3}\equiv \exp[μ(a_{1}% a_{2}-a_{1}^{\dagger}a_{2}^{\dagger})+ν(a_{1}a_{3}-a_{1}^{\dagger}% a_{3}^{\dagger})]${\small . The new 3-mode squeezed vacuum state in Fock space is derived, and the uncertainty relation for it is demonstrated, It turns out that }$S_{3}${\small may exhibit enhanced squeezing. By virtue of the technique of…
Planar squeezed states, i.e. quantum states which are squeezed in two orthogonal spin components, have recently attracted attention due to their applications in atomic interferometry and quantum information [Q. Y. He et al, New J. Phys. 14, 093012 (2012)]. While canonical variables such as quadratures of the radiation field can be squeezed in at most one component, simultaneous squeezing in two orthogonal spin components can be achieved due to the angular momentum commutation relations. We present a novel scheme for planar squeezing via quantum non-demolition (QND) measurements in spin-1 syste…
We derive fidelity benchmarks for the quantum storage and teleportation of squeezed states of continuous variable systems, for input ensembles where the degree of squeezing $s$ is fixed, no information about its orientation in phase space is given, and the distribution of phase space displacements is a Gaussian. In the limit where the latter becomes flat, we prove analytically that the maximal classical achievable fidelity (which is 1/2 without squeezing, for $s=1$) is given by $\sqrt{s}/(1+s)$, vanishing when the degree of squeezing diverges. For mixed states, as well as for general distribut…
This paper reviews quantum spin squeezing, which characterizes the sensitivity of a state with respect to an SU(2) rotation, and is significant for both entanglement detection and high-precision metrology. We first present various definitions of spin squeezing parameters, explain their origin and properties for typical states, and then discuss spin-squeezed states produced with the Ising and the nonlinear twisting Hamiltonians. Afterwards, we explain correlations and entanglement in spin-squeezed states, as well as the relations between spin squeezing and quantum Fisher information, where the …
The squeezed cat state, an essential quantum resource, can be used for quantum error correction and slowing decoherence of the optical cat state. However, preparing a squeezed cat state with high generation rate, and effectively manipulating it, remain challenging. In this work, a high-performance all-optical in-line squeezer is developed to prepare a squeezed cat state and manipulate the phase of the quadrature squeezing. This scheme has the advantages that the phase of the quadrature squeezing of the squeezed cat state can be manipulated by changing the working condition of the squeezer, and…
We investigate the creation of squeezed states of a vibrating membrane or a movable mirror in an opto-mechanical system. An optical cavity is driven by squeezed light and couples via radiation pressure to the membrane/mirror, effectively providing a squeezed heat-bath for the mechanical oscillator. Under the conditions of laser cooling to the ground state, we find an efficient transfer of squeezing with roughly 60% of light squeezing conveyed to the membrane/mirror (on a dB scale). We determine the requirements on the carrier frequency and the bandwidth of squeezed light. Beyond the conditions…
We report on the generation of polarization squeezing of intense, short light pulses using an asymmetric fiber Sagnac interferometer. The Kerr nonlinearity of the fiber is exploited to produce independent amplitude squeezed pulses. The polarization squeezing properties of spatially overlapped amplitude squeezed and coherent states are discussed. The experimental results for a single amplitude squeezed beam are compared to the case of two phase-matched, spatially overlapped amplitude squeezed pulses. For the latter, noise variances of -3.4dB below shot noise in the S0 and the S1 and of -2.8dB i…
We present experimental studies on the generation of pulsed and continuous-wave squeezed vacuum via nonlinear rotation of the polarization ellipse in a $^{87}$Rb vapor. Squeezing is observed for a wide range of input powers and pump detunings on the D1 line, while only excess noise is present on the D2 line. The maximum continuous-wave squeezing observed is -$ 1.4 \pm0.1$ dB (-2.0 dB corrected for losses). We measure -1.1 dB squeezing at the resonance frequency of the $^{85}$Rb $F=3 \to F'$ transition, which may allow the storage of squeezed light generated by $^{87}$Rb in a $^{85}$Rb quantum …
Squeezing of light's quantum noise requires temporal rearranging of photons. This again corresponds to creation of quantum correlations between individual photons. Squeezed light is a non-classical manifestation of light with great potential in high-precision quantum measurements, for example in the detection of gravitational waves. Equally promising applications have been proposed in quantum communication. However, after 20 years of intensive research doubts arose whether strong squeezing can ever be realized as required for eminent applications. Here we show experimentally that strong squeez…
We study continuous variable coherence of phase-dependent squeezed state based on an extended Hanbury Brown-Twiss scheme. High-order coherence is continuously varied by adjusting squeezing parameter $r$, displacement $α$, and squeezing phase $θ$. We also analyze effects of background noise $γ$ and detection efficiency $η$ on the measurements. As the squeezing phase shifts from 0 to $π$, the photon statistics of the squeezed state continuously change from the anti-bunching ($g^{(n)}<1$) to super-bunching ($g^{(n)}>n!$) which shows a transition from particle nature to wave nature. The experiment…
We report the first direct experimental characterization of continuous variable quantum Stokes parameters. We generate a continuous wave light beam with more than 3 dB of simultaneous squeezing in three of the four Stokes parameters. The polarization squeezed beam is produced by mixing two quadrature squeezed beams on a polarizing beam splitter. Depending on the squeezed quadrature of these two beams the quantum uncertainty volume on the Poincaré sphere became a `cigar' or `pancake'-like ellipsoid.
We use a reservoir engineering technique based on two-tone driving to generate and stabilize a quantum squeezed state of a micron-scale mechanical oscillator in a microwave optomechanical system. Using an independent backaction evading measurement to directly quantify the squeezing, we observe $4.7\pm0.9$ dB of squeezing below the zero-point level, surpassing the 3 dB limit of standard parametric squeezing techniques. Our measurements also reveal evidence for an additional mechanical parametric effect. The interplay between this effect and the optomechanical interaction enhances the amount of …
The sensitivity properties of an SU(1,1) interferometer made of two cascaded parametric amplifiers, as well as of an ordinary SU(2) interferometer preceded by a squeezer and followed by an anti-squeezer, are theoretically investigated. Several possible experimental configurations are considered, such as the absence or presence of a seed beam, direct or homodyne detection scheme. In all cases we formulate the optimal conditions to achieve phase super-sensitivity, meaning a sensitivity overcoming the shot-noise limit. We show that for a given gain of the first parametric amplifier, unbalancing t…
We have developed a quantum memory technique that is completely compatible with current quantum information processing for continuous variables of light, where arbitrary frequency sidebands of a squeezed vacuum can be stored and retrieved using bichromatic electromagnetic induced transparency. 2MHz sidebands of squeezed vacuum pulses with temporal widths of 470ns and a squeezing level of -1.78 +- 0.02dB were stored for 3us in the laser-cooled 87Rb atoms. -0.44 +- 0.02dB of squeezing was retrieved, which is the highest squeezing ever reported for a retrieved pulse.
Continuous-wave squeezed states of light at the wavelength of 1550 nm have recently been demonstrated, but so far the obtained factors of noise suppression still lag behind today's best squeezing values demonstrated at 1064 nm. Here we report on the realization of a half-monolithic nonlinear resonator based on periodically-poled potassium titanyl phosphate which enabled the direct detection of up to 12.3 dB of squeezing at 5 MHz. Squeezing was observed down to a frequency of 2 kHz which is well within the detection band of gravitational wave interferometers. Our results suggest that a long-ter…
We present a scheme for the charging of a quantum battery based on the dynamics of an open quantum system undergoing coherent quantum squeezing and affected by an incoherent squeezed thermal bath. We show that quantum coherence, as instigated by the application of coherent squeezing, are key in the determination of the performance of the charging process, which is efficiency-enhanced at low environmental temperature and under a strong squeezed driving.
In this paper we present a pure algebraic construction of the normal factorization of multimode squeezed states and calculate their inner products. This procedure allows one to orthonormalize bases generated by squeezed states. We calculate several correct representations of the normalizing constant for the normal factorization, discuss an analogue of the Maslov index for squeezed states, and show that the Jordan decomposition is a useful mathematical tool for problems with degenerate Hamiltonians. As an application of this theory we consider a non-trivial class of squeezing problems which are…
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…
Using a quantum theory for an ensemble of three-level atoms (lambda) placed in an optical cavity abd driven by electromagnetic fields, we show that the long-lived spin associated with the ground state sublevels can be squeezed. Two kinds of squeezing are obtained: self-spin squeezing, when the input fields are coherent states and the atomic ensemble exhibit a large non-linearity; squeezing transfer, when one of the incoming fields is squeezed.
We report an efficient mechanism to generate a squeezed state of a mechanical mirror in an optomechanical system. We use especially tuned parametric amplifier (PA) inside the cavity and the parametric photon phonon processes to transfer quantum squeezing from photons to phonons with almost 100\% efficiency. We get 50\% squeezing of the mechanical mirror which is limited by the PA. We present analytical results for the mechanical squeezing thus enabling one to understand the dependence of squeezing on system parameters like gain of PA, cooperativity, temperature. As in cooling experiments the d…
We propose a procedure for tomographic characterization of continuous variable quantum operations which employs homodyne detection and single-mode squeezed probe states with a fixed degree of squeezing and anti-squeezing and a variable displacement and orientation of squeezing ellipse. Density matrix elements of a quantum process matrix in Fock basis can be estimated by averaging well behaved pattern functions over the homodyne data. We show that this approach can be straightforwardly extended to characterization of quantum measurement devices. The probe states can be mixed, which makes the pr…
We demonstrate vacuum squeezing at the D1 line of atomic rubidium (795 nm) with a tunable, doubly-resonant, monolithic sub-threshold optical parametric oscillator in periodically-poled Rb-doped potassium titanyl phosphate. The squeezing appears to be undiminished by a strong dispersive optical nonlinearity recently observed in this material.
We report the experimental demonstration of polarization squeezed beam at 795 nm by combining a quadrature squeezed beam with a coherent beam. The quadrature squeezed beam is generated by a degenerate optical parametric amplifier based on a PPKTP crystal. Stokes parameter squeezing of -3.8 dB and anti squeezing of +5.0 dB is observed. This polarization squeezed beam resonant to rubidium D1 line has potential applications in quantum information networks and precise measurement beyond the shot noise limit.
The Stokes-parameter operators and the associated Poincare sphere, which describe the quantum-optical polarization properties of light, are defined and their basic properties are reviewed. The general features of the Stokes operators are illustrated by evaluation of their means and variances for a range of simple polarization states. Some of the examples show polarization squeezing, in which the variances of one or more Stokes parameters are smaller than the coherent-state value. The main object of the paper is the application of these concepts to bright squeezed light. It is shown that a ligh…
Applying stochastic differential equations, we study the squeezing and statistical properties of the cavity and output modes of a degenerate three-level laser whose cavity contains a parametric amplifier and coupled to a squeezed vacuum reservoir. We consider the case in which the top and bottom levels of the three-level cascade atoms injected into the cavity are coupled by the pump mode emerging from the parametric amplifier. It turns out that the presence of the squeezed vacuum reservoir and the parametric amplifier contribute considerably to the mean photon number and the degree of squeezin…
We investigate the time evolution of nonlocality for a two-mode squeezed state in the thermal environment. The initial two-mode pure squeezed state is nonlocal with a stronger nonlocality for a larger degree of squeezing. It is found that the larger the degree of initial squeezing is, the more rapidly the squeezed state loses its nonlocality. We explain this by the rapid destruction of quantum coherence for the strongly squeezed state.
The compatibility of cavity-generated spin-squeezed atomic states with atom-interferometric sensors that require freely falling atoms is demonstrated. An ensemble of $500,000$ spin-squeezed atoms in a high-finesse optical cavity with near-uniform atom-cavity coupling is prepared, released into free space, recaptured in the cavity, and probed. Up to $\sim$10 dB of metrologically-relevant squeezing is retrieved for 700 microsecond free-fall times, and decaying levels of squeezing are realized for up to 3 millisecond free-fall times. The degradation of squeezing results from loss of atom-cavity c…
We analyze the effect of squeezing the channel in binary communication based on Gaussian states. We show that for coding on pure states, squeezing increases the detection probability at fixed size of the strategy, actually saturating the optimal bound already for moderate signal energy. Using Neyman-Pearson lemma for fuzzy hypothesis testing we are able to analyze also the case of mixed states, and to find the optimal amount of squeezing that can be effectively employed. It results that optimally squeezed channels are robust against signal-mixing, and largely improve the strategy power by comp…
We investigate various types of squeezing in a collective su(2J+1) system consisting of spin-J particles (J>1/2). We show that the squeezing in the collective su(2J+1) system can be classified into unitary equivalence classes, each of which is characterized by a set of squeezed and anti-squeezed observables forming an su(2) subalgebra in the su(2J+1) algebra. The dimensionality of the unitary equivalence class is fundamentally related to its squeezing limit. We also demonstrate the classification of the squeezing among the spin and multipolar observables in a collective su(4) system.
We demonstrate a diode-laser-pumped system for generation of quadrature squeezing and polarization squeezing. Due to their excess phase noise, diode lasers are challenging to use in phase-sensitive quantum optics experiments such as quadrature squeezing. The system we present overcomes the phase noise of the diode laser through a combination of active stabilization and appropriate delays in the local oscillator beam. The generated light is resonant to the rubidium D1 transition at 795nm and thus can be readily used for quantum memory experiments.
Residual-Squeezing Mechanism of Mismatch in Inverse-Squeezing Kennedy Receivers
Information Support Force Engineering University(信息支援部队工程大学);Guangxi Key Laboratory of Multimedia Communications and Network Technology, Guangxi University(广西大学);Wuhan Maritime Communication Research Institute(武汉航海通信研究所)
We consider a finite-time quantum Otto heat engine that consists of two isochoric (thermal-contact) process, where the system is alternatively coupled to a hot squeezed and a cold thermal reservoir, and two unitary driven strokes, where the system is isolated from these two baths and its von Neumann entropy keeps constant. Both quantum inner friction and coherence are generated along the driven stroke and coherence cannot be fully erased after the finite-time hot isochore. Using full counting statistics, we present the probability distribution functions of heat injection and total work per cyc…
One of the most fundamental quantum states of light is squeezed vacuum, in which noise in one of the quadratures is less than the standard quantum noise limit. Significant progress has been made in the generation of optical squeezed vacuum and its utilization for numerous applications. However, it remains challenging to generate, manipulate, and measure such quantum states in nanophotonics with performances required for a wide range of scalable quantum information systems. Here, we overcome this challenge in lithium niobate nanophotonics by utilizing ultrashort-pulse phase-sensitive amplifiers…
We present the observation of optical fields carrying squeezed vacuum states at sideband frequencies from 10Hz to above 35MHz. The field was generated with type-I optical parametric oscillation below threshold at 1064nm. A coherent, unbalanced classical modulation field at 40MHz enabled the generation of error signals for stable phase control of the squeezed vacuum field with respect to a strong local oscillator. Broadband squeezing of approximately -4dB was measured with balanced homodyne detection. The spectrum of the squeezed field allows a quantum noise reduction of ground-based gravitatio…
As a genuine many-body entanglement, spin squeezing (SS) can be used to realize the highly precise measurement beyond the limit constrained by classical physics. Its generation has attracted much attention recently. It was reported that $N$ two-level systems (TLSs) located near a one-dimensional waveguide can generate a SS by using the mediation effect of the waveguide. However, a coherent driving on each TLS is used to stabilize the SS, which raises a high requirement for experiments. We here propose a scheme to generate stable SS resorting to neither the spin-spin coupling nor the coherent d…