Quantum state engineering using conditional measurement on a beam splitter

State preparation via conditional output measurement on a beam splitter is studied, assuming the signal mode is mixed with a mode prepared in a Fock state and photon numbers are measured in one of the output channels. It is shown that the mode in the other output channel is prepared in either a photon-subtracted or a photon-added Jacobi polynomial state, depending upon the difference between the number of photons in the input Fock state and the number of photons in the output Fock state onto which it is projected. The properties of the conditional output states are studied for coherent and squeezed input states, and the probabilities of generating the states are calculated. Relations to other states, such as near-photon-number states and squeezed-state-excitations, are given and proposals are made for generating them by combining the scheme with others. Finally, effects of realistic photocounting and Fock-state preparation are discussed. Received: 17 March 1998 / Revised and Accepted: 8 May 1998     

Quantum entanglement of Fock states with perfectly efficient ultraslow single-probe photon four-wave mixing

We propose a method to achieve quantum entanglement of two Fock states with perfectly efficient, ultraslow propagation enhanced four-wave mixing. A cold atomic medium is illuminated with a two-mode cw control laser to produce coherent mixtures of excited states. An ultraslowly propagating, single-photon quantum probe field completes the four-wave mixing with 100% photon flux conversion efficiency, creating a depth dependent entanglement of two Fock states. We show that at a suitable propagation distance, a maximum entangled state is created with a single-photon wave-packet state that has 50% probability of being in each of two product-type Fock states.     

基于量子测量的Fock态制备和自相位调制的影响

提出一种制备Fock态的新方案研究在包含有自相位调制的Kerr介质中两束光的相互作用,信号光场和探测光场初始处于相干态,经由非线性相互作用后演化成为纠缠态.若对探测光场的正交位相分量实行第一类量子测量,信号光场的光子数分布会受到调制.重复上述过程,发现信号光场最终演化成为一个纯的Fock态.这种制备Fock态的原理是基于互相位调制,而自相位调制则起着阻碍Fock态形成的作用.     

Optical mode characterization of single photons prepared by means of conditional measurements on a biphoton state

A detailed theoretical analysis of the spatiotemporal mode of a single photon prepared via conditional measurements on a photon pair generated in the process of parametric down-conversion is presented. The maximum efficiency of coupling the photon into a transform-limited classical optical mode is calculated and ways for its optimization are determined. An experimentally feasible technique of generating the optimally matching classical mode is proposed. The theory is applied to a recent experiment on pulsed homodyne tomography of the single-photon Fock state [A.I. Lvovsky et al., Phys. Rev. Lett. 87, 050402 (2001)]. Received 16 July 2001     

Stochastic quantum trajectories in a QND measurement of photon number

An analysis is presented of the time evolution of an optical field during a quantum nondemolition measurement of photon number using the cross-Kerr interaction between the signal and probe fields. It is shown that the signal field state collapses into a Fock state only asymptotically (in the infinite time limit), remaining in a superposition of two Fock states (Fock-state qubit) throughout most of the measurement period. Estimates are obtained both for the time required to measure photon number to the desired accuracy and for the Fock-state qubit lifetime.     

Generation of a displaced qubit and entangled displaced photon state via conditional measurement and their properties

We study optical schemes for generating both a displaced photon and a displaced qubit via conditional measurement. Combining one mode prepared in different microscopic states (one-mode qubit, single photon, vacuum state) and another mode in macroscopic states (coherent state, single photon added coherent state), a conditional state in the other output mode exhibits properties of a superposition of the displaced vacuum and a single photon. We propose to use the displaced qubit and entangled states composed of the displaced photon as components for quantum information processing. Basic states of such a qubit are distinguishable from each other with high fidelity. We show that the qubit reveals both microscopic and macroscopic properties. Entangled displaced states with a coherent phase as an additional degree of freedom are introduced. We show that additional degree of freedom enables to implement complete Bell state measurement of the entangled displaced photon states.     

Demonstrating various quantum effects with two entangled laser beams

We report on the preparation of entangled two mode squeezed states of yet unseen quality. Based on a measurement of the covariance matrix we found a violation of the Reid and Drummond EPR-criterion at a value of only 0.36 ± 0.03 compared to the threshold of 1. Furthermore, quantum state tomography was used to extract a single photon Fock state solely based on homodyne detection, demonstrating the strong quantum features of this pair of laser-beams. The probability for a single photon in this ensemble measurement exceeded 2/3.     

Dynamics of dispersive photon-number QND measurements in a micromaser

A numerical analysis of dispersive quantum nondemolition measurement of the photon number of a microwave cavity field is presented. Simulations show that a key property of the dispersive atom-field interaction used in Ramsey interferometry is the extremely high sensitivity of the dynamics of atomic and field states to basic parameters of the system. When a monokinetic atomic beam is sent through a microwave cavity, a qualitative change in the field state can be caused by an uncontrollably small deviation of parameters (such as atom path length through the cavity, atom velocity, cavity mode frequency detuning, or atom-field coupling constants). The resulting cavity field can be either in a Fock state or in a super-Poissonian state (characterized by a large photon-number variance). When the atoms have a random velocity spread, the field is squeezed to a Fock state for arbitrary values of the system’s parameters. However, this makes detection of Ramsey fringes impossible, because the probability of detecting an atom in the upper or lower electronic state becomes a random quantity almost uniformly distributed over the interval between zero and unity, irrespective of the cavity photon number.     

Quantum atomic-fluctuations reduction and squeezed-state generation via forward degenerate four-wave mixing

It is shown that correlation of quantum atomic fluctuations for coupled modes at forward degenerate four-wave mixing leads to atomic noise reduction from the in-phase quadrature variance of the mode which is a linear combination of the coupled signal and probe modes. Thus, quantum atomic fluctuations are not an obstacle for the squeezed-state generation via degenerate four-wave mixing.     

Generating and probing a two-photon fock state with a single atom in a cavity

A two-photon Fock state is prepared in a cavity sustaining a "source mode" and a "target mode," with a single circular Rydberg atom. In a third-order Raman process, the atom emits a photon in the target while scattering one photon from the source into the target. The final two-photon state is probed by measuring by Ramsey interferometry the cavity light shifts induced by the target field on the same atom. Extensions to other multiphoton processes and to a new type of micromaser are briefly discussed.     

Efficient generation of correlated photon pairs in a microstructure fiber

We report efficient generation of correlated photon pairs through degenerate four-wave mixing in a microstructure fiber. With 735.7 nm pump pulses producing correlated signal (688.5 nm) and idler (789.8 nm) photons in a 1.8 m microstructure fiber, we detect photon pairs at a rate of 37.6 kHz with a coincidence/ accidental contrast of 10:1 with deltalambda = 0.7 nm. This is the highest rate to our knowledge reported to date in a fiber-based photon source. The light source is highly nonclassical as defined by the Zou-Wang-Mandel inequality, which is violated by 1100 times the uncertainty.     

PREPARATION OF NONCLASSICAL STATES OF A CAVITY FIELD BASED ON A NONLINEAR JAYNES-CUMMINGS MODEL

It is proven in this paper that some kinds of nonclassical quantum states of the cavity field, such as Schr?dinger cat state (amplitude cat or phase cat), sub-Poissonian photon distribution and Fock state, etc., can be generated by conditional meas urements on atoms in the two-photon Jaynes-Cummings model with a Kerr-like medium. The nonlinear constant plays the key modulation role in the preparation of the quantum states, which gives a new controllable parameter for further experi mental researches in this field.     

远程控制纠缠原子的偶极压缩

考虑初始处于EPR态的两个二能级原子A、B,将B原子注入处于真空态和单光子态的叠加态的腔中,演化一段时间后,对B原子进行选择性测量,通过选择合适的腔场初始叠加状态和演化时间,可控制原子A的偶极矩压缩效应.     

Theoretical study on phase conjugation in weakly injected vertical-cavity surface-emitting lasers

This paper gives a detailed theoretical investigation on phase conjugation induced by nearly degenerate fourwave mixing in single mode vertical-cavity surface-emitting lasers （VCSELs） with weak optical injection. Considering VCSELs that can work in linearly polarized or elliptically polarized states, it derives the theoretical expression of the conjugated field by small signal analysis based on the vectoral rate equations-the spin-flip model. For linearly polarized state, VCSELs show similar conjugate spectra to edge-emitting semiconductor lasers. For the elliptically polarized state, dichroism and birefringence parameters as well as the spin-flip rate can change the conjugate spectra. Especially, when frequency detuning of the probe and pump waves is between the positive and negative relaxation oscillation frequency, changes are evident. For specific values of parameters, conjugate efficiency between 20 dB to 40 dB are obtained.     

Generation of superpositions of coherent states on a circle

We propose a simple method to obtain a superposition of coherent states on a circle, including Schr?dinger cat states as a special case, via conditional measurement of the state of three level atoms interacting with a one mode cavity field. In the low amplitude limit, very good approximation of Fock states can also be generated in this way. Received: 8 October 1998 / Accepted: 30 October 1998     

Influence of Thickness of Methyl-Orange-Doped Polyvinyl Alcohol Film on Phase Conjugate Matched Filtering

Phase conjugate matched filtering was performed with optical phase conjugation in Fourier-transforming backward degenerate four-wave mixing. A methyl-orange-doped polyvinyl alcohol (MO/PVA) film was used as a phase conjugator. The influence of the film thickness upon decay of a correlation signal due to phase mismatching was investigated. The thickness was varied from 15 μm to 90 μm. Reduction of the film thickness relaxes the tolerance for phase mismatching, which also occurs when a large reference picture is placed in a pump beam or when a reference picture shifts from the optical axis of the pump beam. Using a MO/PVA film of 15 μm thickness, we obtained allowable angles of 3.4° for a horizontally expanded reference picture and larger than 4.3° for a vertically expanded reference picture, assuming about 40% reduction of a correlation signal is allowable.     

Experimental state tomography of itinerant single microwave photons

A wide range of experiments studying microwave photons localized in superconducting cavities have made important contributions to our understanding of the quantum properties of radiation. Propagating microwave photons, however, have so far been studied much less intensely. Here we present measurements in which we reconstruct the quantum state of itinerant single photon Fock states and their superposition with the vacuum by analyzing moments of the measured amplitude distribution up to fourth order. Using linear amplifiers and quadrature amplitude detectors, we have developed efficient methods to separate the detected single photon signal from the noise added by the amplifier. From our measurement data we have also reconstructed the corresponding Wigner function.     

基于交叉相位调制制备四光子偏振纠缠态及其在隐形传态上的运用

利用克尔介质、偏振分束器、半波片和对强相干探测场的零拍探测,呈现了一个关于制备四光子偏振Diche态、GHZ态和W态的方案,当前量子光学实验技术条件均能有效满足该方案的要求.强的探测模相继和多个信号模光子相互作用,每次对于探测模而言,都会产生一个相位旋转.接下来,对探测模利用零拍探测,信号模可以投影得到想要的光子偏振纠缠态.此外,为了展现所制备的纠缠态作为重要的量子信息资源的价值,基于交叉相位调制进一步提出了一个隐形传送三光子偏振纠缠态的实验方案.     

基于交叉相位调制制备四光子偏振纠缠态及其在隐形传态上的运用

利用克尔介质、偏振分束器、半波片和对强相干探测场的零拍探测,呈现了一个关于制备四光子偏振Diche态、GHZ态和W态的方案,当前量子光学实验技术条件均能有效满足该方案的要求.强的探测模相继和多个信号模光子相互作用,每次对于探测模而言,都会产生一个相位旋转.接下来,对探测模利用零拍探测,信号模可以投影得到想要的光子偏振纠缠态.此外,为了展现所制备的纠缠态作为重要的量子信息资源的价值,基于交叉相位调制进一步提出了一个隐形传送三光子偏振纠缠态的实验方案.     

Approximate and Conditional Teleportation of an Unknown Atomic State Without the Bell-state Measurement with Multi-photon Interaction

A scheme for approximately and conditionally teleporting an unknown atomic state via multi-photon interaction in cavity quantum electro dynamics (QED) is proposed. It is the extension of the scheme of Zheng (2004) [Physical Review A69, 064302], which is based on Jaynes–Cummings model in QED and where only a time point of system evolution and the corresponding Fidelity implementing the teleportation are given. In our scheme, the cavity field may be Fock state and the multi-photon interaction Jaynes–Cummings model is used to realize the approximate and conditional teleportation. Our scheme does not involve the Bell-state measurement and an additional atom, only requiring two atoms and one single-mode cavity. The fidelity of the scheme is higher than that of Zheng (2004) [Physical Review A69, 064302]. The scheme may be generalized to not only the teleportation of the state of a cavity mode to another mode by means of a single atom but also the teleportation of the state of a trapped ion. PACS: 03.67.-Ta, 03.65.Ta, 42.50.Dv