The driven oscillator in the photon-number probability representation of quantum mechanics

We study the evolution of the driven harmonic oscillator in the probability representation of quantum mechanics. We use the photon-number tomographic-probability-distribution function to describe the quantum states of the system. We give a general review of the photon-number tomographic framework, including a discussion on the connection with other representations of quantum mechanics. We find tomograms of coherent states as well as excited states of the harmonic oscillator in an explicit form. We discuss the time evolution of the photon-number tomograms and transforms of the propagators for different representations of quantum mechanics. We obtain the propagator for the photon-number tomographic-distribution function for the case of the driven oscillator in an explicit form.     

Photon-number squeezing in circuit quantum electrodynamics

A superconducting single-electron transistor (SSET) coupled to an anharmonic oscillator, e.g., a Josephson junction-L-C circuit, can drive the latter to a nonequilibrium photon-number distribution. By biasing the SSET at the Josephson quasiparticle cycle, cooling of the oscillator as well as a laserlike enhancement of the photon number can be achieved. Here, we show that the cutoff in the quasiparticle tunneling rate due to the superconducting gap, in combination with the anharmonicity of the oscillator, may create strongly squeezed photon-number distributions. For low dissipation in the oscillator, nearly pure Fock states can be produced.     

Quantum estimation of states and operations from incomplete data

We review minimum Kullback entropy principle for estimation of quantum states and operations and discuss its application to qubit and harmonic oscillator systems. In particular, we address the estimation of displacement and squeezing operations from incomplete data and show how to estimate the displacement or squeezing amplitude starting from photon-number resolving or on/off photodetection.     

Quantum and classical correlations in tripartite Gaussian states of light

We demonstrate an optical scheme involving two interlinked nonlinear interactions taking place simultaneously in a second-order nonlinear crystal. The three-mode output state is fully inseparable and endowed with perfect photon-number correlations among the generated fields. In order to discriminate between classical and quantum correlations we evaluate the quantum noise reduction, i.e. compare the fluctuations of the difference photocurrent between one mode and the sum of the other two with those coming from three uncorrelated coherent states. Preliminary results indicate that our scheme may achieve three-mode sub-shot noise correlations with current technology.     

Photon-number fluctuation and correlation of bound soliton pairs in mode-locked fiber lasers

Quantum photon-number fluctuation and correlation of bound soliton pairs in mode-locked fiber lasers are studied on the basis of the complex Ginzburg-Landau equation model. We find that, depending on their phase difference, the total photon-number noise of the bound soliton pair can be larger or smaller than that of a single soliton, and the two solitons in the soliton pair have a corresponding positive or negative photon-number correlation. It is predicted for the first time to our knowledge that out-of-phase soliton pairs can exhibit less noise as a result of negative correlation.     

New approach for deriving the exact time evolution of the density operator for a diffusive anharmonic oscillator and its Wigner distribution function

Using thermal entangled state representation,we solve the master equation of a diffusive anharmonic oscillator(AHO) to obtain the exact time evolution formula for the density operator in the infinitive operator-sum representation.We present a new evolution formula of the Wigner function(WF) for any initial state of the diffusive AHO by converting the WF calculation into an overlap between two pure states in an enlarged Fock space.It is found that this formula is very convenient in investigating the WF’s evolution of any known initial state.As applications,this formula is used to obtain the evolution of the WF for a coherent state and the evolution of the photon-number distribution of diffusive AHOs.     

New approach for deriving the exact time evolution of density operator for diffusive anharmonic oscillator and its Wigner distribution function

Using the thermal entangled state representation, we solve the master equation of a diffusive anharmonic oscillator (AHO) to obtain the exact time evolution formula for the density operator in the infinitive operator-sum representation. We present a new evolution formula of the Wigner function (WF) for any initial state of the diffusive AHO by converting the calculation of the WF to an overlap between two pure states in an enlarged Fock space. It is found that this formula brings us much convenience to investigate the WF's evolution of any known initial state. As applications, this formula is used to obtain the evolution of the WF for a coherent state and the evolution of the photon-number distribution of the diffusive AHO.     

A new type of photon-added squeezed coherent state and its statistical properties

We construct a new type of photon-added squeezed coherent state generated by repeatedly operating the bosonic creation operator on a new type of squeezed coherent state [Fan H Y and Xiao M 1996 Phys. Lett. A 220 81]. We find that its normalization factor is related to single-variable Hermite polynomials. Furthermore, we investigate its statistical properties, such as Mandel’s Q parameter, photon-number distribution, and Wigner function. The nonclassicality is displayed in terms of the intense oscillation of photon-number distribution and the negativity of the Wigner function.     

Optimization of ultrashort-pulse squeezing by spectral filtering with the Fourier pulse-shaping technique

We propose an adaptive waveform-control approach to optimize photon-number squeezing by the nonlinear fiber spectral filtering method. More than -8-dB squeezing of the sech envelope pulse is numerically predicted when the spectral phase is modulated before the pulse is sent to a fiber. The quantum cross correlations of the photon-number fluctuation become uniformly negative when the pulse is optimally shaped.     

光泵三能级原子体系产生光子数压缩态

本文证明光泵三能级原子体系可以产生光子数压缩态。分别计算非相干泵浦、弱相干泵浦和强相于泵浦几种情形下的Fano因数。结果表明,弱相干泵浦时可获得最佳压缩效应,相应的Fano因数为0.16。这种产生光子数压缩态的方法在实验上是简便可行的。 关键词：     

Photon-Number Distributions of Lasers Generated via Pump-Noise Suppression

The photon-number distribution of lasers generated via pump-noise suppression is derived in the photon-number representation. The derivation shows that the negative probability emerging in the calculation of the photon-number distribution in the photon-number representation is not caused by the representation itself but by the truncation of the master equation. Here without truncating the master equation we derive the characteristic function and the distribution function of the photon-number distribution of the laser system with regular pump and with spontaneous atomic decays being eliminated. It is convenient to use the characteristic function to calculate any order of the moment of the photon-number distribution. Such a method can be used to some more general cases, in which the laser system has imperfectly regular pump and the spontaneous atomic decays are also considered.     

Nonlinear interferometry via Fock-state projection

We use a photon-number-resolving detector to monitor the photon-number distribution of the output of an interferometer, as a function of phase delay. As inputs we use coherent states with mean photon number up to seven. The postselection of a specific Fock (photon-number) state effectively induces high-order optical nonlinearities. Following a scheme by Bentley and Boyd [Opt. Express 12, 5735 (2004).10.1364/OPEX.12.005735], we explore this effect to demonstrate interference patterns a factor of 5 smaller than the Rayleigh limit.     

Quantum Nondemolition Measurement of Photon-Number Distribution for a Two-Mode Field

We propose a quantum nondemolition measurement of the photon-number distribution for a two-mode cavity field. In the scheme two sequences of two-level atoms interact dispersively with the respective cavity modes and resonantly with two classical fields, and then are detected continually. The field finally reduces to a two-mode Fock state. The probability of collapsing to a given Fock state is determined by the initial photon-number distribution. The scheme can be easily generalized to a field with N modes.     

Selectivity control of Stark-ladder transitions in asymmetric double-well GaAs/AlAs superlattices by barrier sequence modulation

We have investigated field-induced features of optical transitions in asymmetric double-well superlattices (ADW-SLs) with and without barrier sequence modulation by low-temperature photocurrent (PC) spectroscopy. The difference between the heavy-hole confinement energies in the wide and narrow wells results in two types of Stark-ladder transitions, so that four ±1st-order spatially indirect transitions are expected to exist in the ADW-SL. The oscillator strength of these indirect transitions is affected by the strength and the direction of coupling between the wide and narrow wells. The introduction of the barrier sequence modulation into the ADW-SL realizes the control of these coupling mechanisms. This technique is a new method to modulate the oscillator strength of the indirect Stark-ladder transitions.     

Photon-number dependent cavity vacuum induced transparency and single photon separation

We investigate photon-number dependent cavity vacuum induced transparency and magneto-optical rotation (MOR) in a cavity quantum electrodynamics system, which consists of two cavities and an ensemble of Λ-type atoms. We demonstrate that the probe photon coupled into one cavity can be transferred to the mode of another cavity via coherent Raman scattering. The transmission, the phase shift, as well as the vacuum Rabi splitting therefore strongly depend upon the probe photon number coupled into the cavity. The photon number dependent cavity vacuum induced transparency can be extended into four-level tripod atoms, leading to photon-number dependent MOR. This can be used to separate the single photon from higher photon number components in the direction of polarization and create a deterministic single photon source.     

The Spatial-Temporal Correlations of Resonance Fluorescence

The spatial-temporal correlations of resonant fluorescence from a single two-level atom is studied based on the investigation of different photocurrent correlations after homodyning the fluorescence with a local oscillator. It is found that the nonclassical features of the measured field is position-dependent on the detection plane.     

Phase-sensitive nonclassical properties of photon-added-then-subtracted coherent squeezed states

We investigate the nonclassical properties of the photon-added-then-subtracted coherent squeezed state(PASCSS) via the sub-Poissonian statistics,the photon-number distribution,and the negativity of the Wigner function.It is found that the PASSCS is a superposition state of D(β)S(ζ)|0>,D(β)S(ζ)|1>,and D(β)S(ζ)|2>.We find that the Mandel Q parameter,the photon-number distribution,and the negative volume of the Wigner function of the PASCSS are all periodic functions of the compound φ-θ/2 with a period π involved with squeezing and displacement parameters.     

Experimental demonstration of sub-shot-noise intensity correlations in an intense twin beam

Twin-beam states of light produced by spontaneous parametric downconversion are endowed with sub-shot-noise photon-number correlations at any intensity regime. We have demonstrated sub-shot-noise photon-number correlations in a ps-pulsed intense (more than 1000 photons) twin beam by measuring the variance of the difference in the number of photons detected in the two outputs of the crystal. The variance is 3.25 dB below the shot-noise level. Measurements show that detection of sub-shot-noise correlation requires a careful selection of twin coherence areas and that these areas depend on the pump intensity.     

Tomographic measurement of joint photon statistics of the twin-beam quantum state

We report the first measurement of the joint photon-number probability distribution for a two-mode quantum state created by a nondegenerate optical parametric amplifier. The measured distributions exhibit up to 1.9 dB of quantum correlation between the signal and idler photon numbers, whereas the marginal distributions are thermal as expected for parametric fluorescence.     

Statistical properties of a solvable three-boson squeeze operator model

In the present paper we introduce a new squeeze operator, which is related to the time-dependent evolution operator for Hamiltonian representing mutual interaction between three different modes. Squeezing phenomenon as well as the variances of the photon-number sum and difference are considered. Moreover, Glauber second-order correlation function is discussed, besides the quasiprobability distribution function and phase distribution for different states. The joint photon-number distribution is also reported. Received 29 March 2000 and Received in final form 20 September 2000