Nonclassical Photon Statistics Research Articles

Nonclassical photon statistics

Some nonclassical properties of a particular state of light are demonstrated by computing the Wigner function. A quantum model of generating this state is proposed. A criterion called the distance variation difference is introduced to measure how far any state is from its corresponding coherent state.

Review Article

We present a review of theoretical and experimental aspects of multiphoton quantum optics. Multiphoton processes occur and are important for many aspects of matter–radiation interactions that include the efficient ionization of atoms and molecules, and, more generally, atomic transition mechanisms; system-environment couplings and dissipative quantum dynamics; laser physics, optical parametric processes, and interferometry. A single review cannot account for all aspects of such an enormously vast subject. Here we choose to concentrate our attention on parametric processes in nonlinear media, with special emphasis on the engineering of nonclassical states of photons and atoms that are relevant for the conceptual investigations as well as for the practical applications of forefront aspects of modern quantum mechanics. We present a detailed analysis of the methods and techniques for the production of genuinely quantum multiphoton processes in nonlinear media, and the corresponding models of multiphoton effective interactions. We review existing proposals for the classification, engineering, and manipulation of nonclassical states, including Fock states, macroscopic superposition states, and multiphoton generalized coherent states. We introduce and discuss the structure of canonical multiphoton quantum optics and the associated one- and two-mode canonical multiphoton squeezed states. This framework provides a consistent multiphoton generalization of two-photon quantum optics and a consistent Hamiltonian description of multiphoton processes associated to higher-order nonlinearities. Finally, we discuss very recent advances that by combining linear and nonlinear optical devices allow to realize multiphoton entangled states of the electromagnetic field, either in discrete or in continuous variables, that are relevant for applications to efficient quantum computation, quantum teleportation, and related problems in quantum communication and information.

Highly nonclassical photon statistics in parametric down-conversion

We use photon counters to obtain the joint photon-counting statistics from twin-beam nondegenerate parametric down-conversion, and we demonstrate directly, and with no auxiliary assumptions, that these twin beams are nonclassical.

Nonclassical second-order photon statistics

Various random point processes occurring in the detection of photons are considered. Statistics of the number of points registered within a finite time interval and of the times between these points are analysed. Based on the second order moments of these statistics, new criteria for characterizing classical and nonclassical properties of photon statistics are proposed.

Cavity cooling of atoms: a quantum statistical treatment

A fully quantum mechanical solution of the dissipative motion of an atomic centre-of-mass strongly coupled to a dynamically varying cavity field mode is presented. Beyond the statistical properties, such as the temperature and localization of the atom, the coherence properties of the atomic wave packet and its entanglement to the cavity field are calculated. The latter is the source of a nonclassical photon statistics expressed in terms of the Mandel Q parameter. The trapping time of an atom initially localized in a potential well is found to significantly deviate from the semiclassically expected results, which we attribute to the graininess of the photon field.

Single-Molecule Triplet-State Photon Antibunching at Room Temperature

We have probed single-molecule metal-to-ligand charge transfer (MLCT) dynamics of a ruthenium complex at room temperature. Using photon antibunching measurements under continuous wave (CW) laser excitation, nonclassical photon statistics, and excitation power dependent measurements, we were able to selectively measure the single-molecule MLCT state lifetime. This work demonstrated, as the first single-molecule photon antibunching measurement of the triplet excited state, a new application of single-molecule spectroscopy on excited-state dynamics and ground-state recovering dynamics of an important class of chemical species that have often been used and studied in energy conversion and electron transfer.

Nonclassical photon statistics of the light from a weakly driven cavity containing weakly driven two-level atoms

The photon statistics of the light transmitted from a weakly driven optical cavity containing weakly driven identical two-level atoms are investigated. The second-order intensity correlation function for the light is derived analytically in the case of purely radiative atomic decay and is numerically calculated in the case taking into account atomic nonradiative dephasing. It is shown that large nonclassical effects can be obtained even in the weak coupling regime by choosing the ratio between the amplitudes of the two driving fields.

Photon-bunching, photon-antibunching and the nonclassical photon statistics of coherent light coupled to a driven harmonic oscillator of time dependent mass and frequency

The analytical solution of the quantum driven harmonic oscillator of time dependent mass and frequency (DHTDMF) is exploited to obtain the photon-bunching, photon-antibunching and the nonclassical photon statistics of the input coherent light coupled to the oscillator. We observe that the model Hamiltonian of a DHTDMF coincides with those of the model Hamiltonian of a two-photon coherent state due to H.P. Yuen [Phys. Rev. A 13 (1976) 226]. To substantiate our analytical results, we give a special case corresponding to a damped harmonic oscillator subject to an external periodic force. The quantum statistical properties of the radiation field are discussed for under-, over-, and for critically-damped situations of the oscillator coupled to an initial coherent field. The off-resonance and the near- or on-resonance of the oscillator with respect to the frequency of the external force are discussed. In the determination of quantum statistical properties of the radiation field, we observe that the effects of the driving force are important only when the frequency of the oscillator is in near- or in on-resonance condition with that of the frequency of the external periodic force.

Approximate quantum statistical properties of a nonlinear optical coupler

An asymmetric optical coupler, arising out of the combination of a linear and a quadratic waveguides, is exploited to study the quantum statistical properties of the input coherent light passing through it. The Heisenberg equation of motion for the field operators are found to give coupled nonlinear differential equations. Under the weak field approximations, these coupled differential equations are solved by using an intuitive approach. The solution for the field operators are used to obtain the analytical expressions for squeezing, photon bunching, photon antibunching and the nonclassical photon statistics of the input coherent light. These analytical expressions are quite complicated to draw any conclusions. To keep up the analytical flavour, we simplify them further to discuss the squeezing, photon bunching, photon antibunching and nonclassical photon statistics of the input coherent light in single and compound field modes.

Tomography of nonclassical states

A review of the symplectic tomography method is presented. Superpositions of different types of photon states are considered within the framework of the tomography approach. Such nonclassical photon states as even and odd coherent states, crystallized Schrodinger cat states, and other superposition states are studied using the construction of symplectic tomograms (tomographic symbols) and the star-product formalism for tomograms.

Dynamics of Quantized Photon and Electron Field in Semiconductor Multi-Subbands Superlattices

We study time evolution of the interacting system consisting of quantized photon field and electron field in semiconductor superlattices analytically/numerically. In the single-subband condition, the electron dynamics is able to generate several nonclassical photon states depending on the external dc bias. Effects of the intersubband transition for the quantized photon states is investigated in the multi-subband condition. Competition of two-kinds of intersubband electron dynamics, Rabi oscillation and Zener tunneling, is discussed.

Observation of nonclassical photon statistics due to quantum interference.

Phase-dependent photon statistics is observed in the mixed field of a narrow band two-photon source and a coherent field. At a certain phase, the nonclassical effect of photon antibunching occurs while at another the photon bunching effect appears. Furthermore, we observed a novel nonclassical phenomenon that exhibits more complex structure. The different features in photon statistics are attributed to a two-photon interference effect.

Quantum jump induced non-classical photon statistics of fluorescence light emitted by cold helium atoms in an optical lattice: coherent control by polarization gradient and an axial magnetic field

We report on the theoretical calculations of the effect of the polarization gradient and an axial magnetic field on quantum noise reduction and quantum jumps in the resonance fluorescence emitted by cold metastable helium atoms confined in an optical lattice. We find that the localization of the atoms in the optical lattice destroys the non-classical properties of the emitted light but can be recovered in the presence of an axial magnetic field. The polarization gradient induces electron shelving at selected points (z = nλ/4) on the optical lattice. At these selected points, squeezing is maximized.

Photon statistics in single-molecule fluorescence at room temperature

The fluorescence of single terrylene molecules in a crystalline host is investigated at room temperature by scanning confocal optical microscopy. Photon arrival times are analyzed in terms of inter-photon time distribution, second-order correlation function, and Mandel's Q-function. Nonclassical photon statistics is observed and a reverse intersystem crossing is detected that accelerates linearly with the applied laser power. Rate equations for the time evolution of the molecular level populations are shown to be appropriate for the analysis of the observations.

Dipole blockade and quantum information processing in mesoscopic atomic ensembles.

We describe a technique for manipulating quantum information stored in collective states of mesoscopic ensembles. Quantum processing is accomplished by optical excitation into states with strong dipole-dipole interactions. The resulting "dipole blockade" can be used to inhibit transitions into all but singly excited collective states. This can be employed for a controlled generation of collective atomic spin states as well as nonclassical photonic states and for scalable quantum logic gates. An example involving a cold Rydberg gas is analyzed.

Construction of Classical and Non-classical Coherent Photon States

It is well known that the diagonal matrix elements of all-order coherent states for the quantized electromagnetic field have to constitute a Poisson distribution with respect to the photon number. The present work gives first the summary of a constructive scheme, developed previously, which determines in terms of an auxiliary Hilbert space all possible off-diagonal elements for the all-order coherent density operators in Fock space and which identifies all extremal coherent states. In terms of this formalism it is then demonstrated that each pure classical coherent state is a uniformly phase locked (quantum) coherent superposition of number states. In a mixed classical coherent state the exponential of the locked phase is shown to be replaced by a rather arbitrary unitary operator in the auxiliary Hilbert space. On the other hand classes for density operators—and for their normally ordered characteristic functions—of non-classical coherent states are obtained, especially by rather weak perturbations of classical coherent states. These illustrate various forms of breaking the classical uniform phase locking and exhibit rather peculiar properties, such as asymmetric fluctuations for the quadrature phase operators. Several criteria for non-classicality are put forward and applied to the elaborated non-classical coherent states, providing counterexamples against too simple arguments for classicality. It is concluded that classicality is only a stable concept for coherent states with macroscopic intensity.

Entanglement, interference, and measurement in a degenerate parametric oscillator.

Quantum dynamical equations of motion for homodyne detection of the degenerate optical parametric oscillator are solved exactly. Nonclassical photon statistics are shown to be a consequence of interference of probability amplitudes, entanglement of photon pairs from such an oscillator, and the role of measurement in quantum evolution.

Nonclassical radiation from a single self-assembled InAs quantum dot

We report the experimental observation of photon antibunching in fluorescence from a single self-assembled InAs quantum dot. The nonclassical photon statistics proves the atomlike nature of a single quantum dot at cryogenic temperatures. Pump-power-dependent measurements of the correlation function ${g}^{(2)}(\ensuremath{\tau})$ provide a method to determine the recombination time of the single exciton ground-state transition that does not require pulsed lasers. Using this method, we investigate the influence of photonic environment on a single quantum dot exciton lifetime.

Control of quantized photon states with external dc bias in semiconductor superlattices

We show that the Bloch oscillation in semiconductor superlattices under the external dc bias is able to generate nonclassical photon states. The time development operator of the photon field in such systems is obtained and is shown to be equivalent approximately to the displacement operator, the phase-quadrature amplitude squeezing operator, or the optical Kerr operator, depending on the external dc bias. Such equivalence is discussed also in terms of Stark-ladder formation.

Non-classical photon statistics for two-mode optical fields

Non-classical photon statistics for two-mode optical fields