Two-photon Coherent States Research Articles

Higher-order criteria for nonclassical effects in photon statistics.

Based on inequalities derived from the partial ordering by majorization, some higher-order criteria for the existence of nonclassical effects in photon statistics are introduced. These generalize the well-known concept of two-photon antibunching to many-photon antibunching. The photon-number distribution of the famous two-photon coherent state is used to illustrate these new criteria.

Multimode two-photon coherent states and unitary representation of the symplectic group

Pure coherent squeezed states of many degrees of freedom are analyzed via a fluctuation matrix description and a symplectic group description.

Properties of quantum communication with received quantum state control

The advantage of nonstandard quantum states such as two-photon coherent state (or squeezed states) and photon number state as transmitter state is strongly degraded by transmission loss in quantum communications. To cope with such a problem, a new application of these states is proposed, and it is shown that its system has infinite capacity.

Coherent two-photon transitions in Rydberg atoms in a cavity with finite Q.

The effects of the cavity damping on the phenomenon of collapse and revival in the population inversion of an atom in a two-photon process are investigated by using the dressed-atom approximation. Explicit results are given for a field initially in either a coherent or a two-photon coherent state. The cavity damping is expected to have more significant effects on two-photon transitions because the vacuum-field Rabi frequency for two-photon transitions is smaller than that for single-photon transitions.

A squeezed-state primer

Using only elementary quantum-mechanical concepts, the statistical properties of various harmonic oscillator states that are linear superpositions of its energy eigenfunctions are described. These superpositions include coherent states and squeezed (or two-photon coherent) states. The resulting Gaussian, minimum-uncertainty wave packets are shown to oscillate back and forth for both coherent and squeezed states, but with an oscillating ‘‘width’’ for the squeezed states. Also examined are the principles underlying the production of squeezed electromagnetic waves via parametric amplification or four-wave mixing, their measurement by homodyne detection, and the connection between squeezing and non-Poissonian counting statistics.

Entropy of Optical Fields

A systematic approach to the use of entropy as a measure of noise and order in quantum optical fields is developed. The general definition of entropy, adopting the density matrix, is expressed in terms of both the eigenvalues of this operator and the quasidistribution function related to antinormal ordering of the field operators. Special states of optical fields, such as the Fock state, the coherent state, the chaotic state, single-mode and multimode two-photon coherent states, squeezed states and the shifted gaussian state, including the time development under a particular interaction, are considered. The general conclusions reached are illustrated by numerical results.

Degenerate four-wave mixing as a possible source of squeezed-state light

The suitability of degenerate four-wave mixing (DFWM) as a source of squeezed-state (two-photon coherent state) light is investigated, both theoretically and experimentally. In previous semiclassical theory, which neglected pump quantization and loss in the nonlinear medium, Yuen and Shapiro [Opt. Lett. 4, 334 (1979)] showed that such states would be generated by 50%-50% combination of the transmitted probe (TP) and the phase-conjugate (PC) output beams of DFWM. Here the effects of quantum fluctuations in the amplitudes and phases of the pump beams are calculated in a traveling-wave finite-interaction-length DFWM configuration. It is shown that in the limit of strong pump beams and weak nonlinear coupling, the classical-pumps assumption of Yuen and Shapiro is valid. With use of this assumption, loss in the nonlinear medium is incorporated into the model by coupling the interacting modes to a set of reservoir modes. It is shown that loss presents an absolute limit on the degree of squeezing that can be achieved with DFWM. Also, for comparison with experimental work, the photoelectron statistics of the TP, PC, and 50%-50% combination modes are calculated for lossy DFWM; significant deviations are found from the predictions for lossless operation. Quantum-noise measurements on the PC and TP beams generated in sodiumvapor DFWM are described. The mixer is pumped and probed by the nearly transform-limited pulses produced by a continuous-wave-oscillator-pulse-amplifier chain dye laser at 589 nm wave-length. The normalized second-factorial moment ${g}_{2}$ of the PC and TP beams is determined from photoelectron-counting measurements. Inability to simultaneously achieve high DFWM reflectivity and acceptably low scattered-plus-fluorescent background, coupled with low photomultiplier quantum efficiency, restrict the experiment to a DFWM regime wherein theory predicts Poisson statistics. Experimental ${g}_{2}$ values corroborate this prediction, indicating that systematic and excess noises have been eliminated. No attempt was made to measure the quantum statistics of the 50%-50% combination mode.

Phase and amplitude uncertainties in heterodyne detection

The quantum limits on simultaneous phase and squared-amplitude measurements made via optical heterodyne detection on a single-mode radiation field are established. The analysis proceeds from a fully quantum mechanical treatment of heterodyning with ideal photon detectors. A high mean field uncertainty principle is proven for simultaneous phase and squared-amplitude observations under the condition that the signal and image band states are independent, and the image band has zero mean. Operator representations are developed which show that no such principle applies when arbitrary signal/image band dependence is permitted, although the mean observations are no longer functions of the signal field alone. A multimode two-photon coherent state illustrating this behavior at finite energy is exhibited. Potential applications for the resulting improved accuracy measurements are briefly described.

Comment on new coherent states with applications to time-dependent systems

It is shown that the new class of coherent states defined by Rajagopal and Marshall is equivalent to the well-known two-photon coherent states.

Contractive States and the Standard Quantum Limit for Monitoring Free-Mass Positions

The familiar minimum-uncertainty wave packets for masses are generalized in analogy with the two-photon coherent states of the radiation field. The free evolution of a subclass of these states, the contractive states, leads to a narrowing of the position uncertainty in contrast with the usual minimum-uncertainty wave packets. As a consequence the standard quantum limit for monitoring the positions of a free mass can be breached. Further implications on quantum nondemolition measurements are discussed.

On the Photon Statistics of Two-photon Stimulated Emission

Using the generalized Fokker-Planck equation approach it is shown that two-photon stimulated emission cannot be a source of light exhibiting antibunching of photons and therefore the two-photon coherent states, also providing antibunching, cannot serve as a fully appropriate description of two-photon stimulated emission, if losses are not considered.

Comparative performance of quantum signals in unimodal and bimodal binary optical communications

The performance of two-photon coherent-state (TCS) signals and integral-quantum signals in unimodal and bimodal free-space optical communications is compared with that of ordinary ,coherent signals under the constraint of fixed average error probability. For the unimodal channel of known phase the minimum attainable error probability for both on-off and antipodal TCS signals received in thermal noise is calculated by applying perturbation theory to the detection operator equation. For unimodal antipodal TCS signaling the threshold receiver is also considered. For channels of random phase the optimum photon-counting receiver is analyzed. In all cases the advantage of the nonclassical signal over an ordinary coherent signal vanishes as the transmittance of the channel goes to zero.

Coherent Properties of the Two-Photon Coherent State

Photon anti-bunching of the two-photon coherent state (TCS) is investigated under the variation of parameters. It appears that the effect of anti-bunching is less for stronger intensity of the radiation. Since two-photon laser has not been realized yet, detection or the TCS should be carried out for the radiation through matter in which as a result of interaction the TCS might be created, i.e., hybrid radiation containing the TCS. The second-order coherence of the hybrid radiation consisting of TCS and blackbody radiation is discussed. Numerical results are shown in several figures.

Quantum statistical properties of the radiation field in the degenerate two-photon emission process

The degenerate two-photon emission process is treated on the basis of quantum theory. Neglecting relaxation mechanisms, solutions in short time approximation are given. Relevant quantities as the mean photon number, second order correlation, field fluctuations and the uncertainty product are analyzed. It is shown, that an initial coherent state does not tend to a two-photon coherent state by two-photon emission as it can be expected from the results given by Yuen.

Connection between generalized glauber operators and two-photon coherent states of the radiation field

Connection between generalized glauber operators and two-photon coherent states of the radiation field

Optical communication with two-photon coherent states--Part III: Quantum measurements realizable with photoemissive detectors

In Part I of this three-part study it was shown that the use of two-photon coherent state (TCS) radiation may yield siginificant performance gains in free-space optical communicatinn if the receiver makes a quantum measurement of a single field quadrature. In Part II it was shown that homodyne detection achieves the same signal-to-noise ratio as the quantum field quadrature measurement, thus providing a receiver which realizes the linear modulation TCS performance gain found in Part I. Furthermore, it was shown in Part il that ff homodyne detection does exactly correspond to the field quadrature measurement, then a large binary communication performance gain is afforded by homodyne detection of antipodal TCS signals. The full equivalence of honmdyne detection and single-quadrature field measurement, as well as that of heterodyne detection and two-quadrature field measurement, is established. Furthermore, a heterodyne configuration which uses a TCS image-band oscillator in addition to the usual coherent state local oscillator is studied. This coafiguration termed TCS heterodyne detection is shown to realize all the quantum measurements described by arbitrary TCS. The foregoing results are obtained by means of a representation theorem which shows that photoemissive detection realizes the photon flux density measurement.

Detection of Quantum Signals by a Mismatched Receiver

A quantum receiver is modelled as a harmonic oscillator imperfectly matched to the incident signal-bearing field. At the beginning of its interaction with the field the oscillator is primed by being placed in a predetermined quantum state. It is shown how to calculate the state of this oscillator at the end of the observation interval both in the presence and in the absence of an incident coherent signal. As examples the error probabilities of a binary on-off communication system with such a mismatched receiver are calculated (a) for a signal of known phase, the receiver primed with a two-photon coherent state, and (b) for a signal of random phase, the receiver primed with a number eigenstate. In both cases the error probability depends on the mean number of externally available signal photons when the number of photons in the priming state is very large, rather than on the smaller number that would actually be absorbed by the mismatched receiver unprimed.

Two-Photon Coherent-Transient Measurement of the Nonradiative Collisionless Dephasing Rate in SF6via Doppler-Free Degenerate Four-Wave Mixing

This Letter reports, for the first time, an experimental measurement of the collision-less dephasing time of the ${\ensuremath{\nu}}_{3}=2$ level in S${\mathrm{F}}_{6}$ using Doppler-free two-photon degenerate four-wave mixing. The measurement is performed in the time domain by use of a short-pulse C${\mathrm{O}}_{2}$ laser to establish a molecular two-photon coherent state. The coherent state is then probed as a function of time to yield a dephasing time of 1.8 nsec which is related to intramolecular dephasing rates.

Generation and detection of two-photon coherent states in degenerate four-wave mixing

It is shown that degenerate four-wave mixing generates two-photon coherent states (TCS) of the radiation field for modes that are proper combinations of the output object and image waves. TCS light has novel quantum behavior, which can be probed by homodyne detection, intensity interferometry, or photocount statistics. Numerical estimates indicate that the generation and detection of TCS light via degenerate four-wave mixing and homodyne detection can be accomplished with current technology.

Optical communication with two-photon coherent states--Part II: Photoemissive detection and structured receiver performance

In Part I of this three-part study, it was shown that novel quantum states, called two-photon coherent states (TCS), have significant potential for improving free-space optical communications. Because TCS radiation does not possess a classical analog, i.e., its diagonal <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</tex> -representation is highly singular, the semiclassical conditional Poisson process model for direct detection is not applicable to TCS reception. In this paper, photoemissive detection of arbitrary quantized radiation fields is studied with incorporation of the nontrivial effects of detector quantum efficiency. General theorems are derived permitting the application of classical point process results to the detection and estimation of signals in arbitrary quantum states. These general theorems are applied to determining the performance of TCS optical communication systems that employ direct, heterodyne, or homodyne detection in binary decision as well as in linear modulation problems. It is shown that the use of TCS radiation with direct detection or heterodyne detection results in minimal performance increments over comparable coherent-state systems. Homodyne detection, however, can achieve the full TCS signal-to-noise ratio improvement predicted in Part I of this study. The increase in homodyne signal-to-noise ratio obtained by use of TCS radiation yields significant performance gains in both linear modulation and antipodal signal detection.