Order Coherence Function Research Articles

Nonequilibrium Prethermal States in a Two-Dimensional Photon Fluid.

We report on the observation of a prethermal state in a nonequilibrium, two-dimensional fluid of light. Direct measurements of the first order coherence function of the fluid reveal the dynamical emergence of algebraic correlations, a quasi-steady-state with properties close to those of thermal superfluids. By a controlled increase of the fluctuations, we observe a crossover from algebraic to short-range (exponential) correlations. We interpret this phenomenon as a nonequilibrium precursor of the Kosterlitz-Thouless transition.

Quantum coherence on selectivity and transport of ion channels

Recently, it has been suggested that ion channel selectivity filter may exhibit quantum coherence, which may be appropriate to explain ion selection and conduction processes. Potassium channels play a vital role in many physiological processes. One of their main physiological functions is the efficient and highly selective transfer of K+ ions through the membranes into the cells. To do this, ion channels must be highly selective, allowing only certain ions to pass through the membrane, while preventing the others. The present research is an attempt to investigate the relationship between hopping rate and maintaining coherence in ion channels. Using the Lindblad equation to describe a three-level system, the results in different quantum regimes are examined. We studied the distillable coherence and the second order coherence function of the system. The oscillation of distillable coherence from zero, after the decoherence time, and also the behavior of the coherence function clearly show the point that the system is coherent in ion channels with high throughput rates.

Strong-coupling-assisted formation of coherent radiation below the lasing threshold.

The creation of nanoscale lasers that operate above a coherent threshold is a challenging problem. We propose a way to circumvent this issue using systems in which a strong coupling regime is achieved between the light and the active medium. In the strong coupling regime, energy oscillations take place between the EM field in the cavity and the atoms. We show that by applying appropriate time modulation to the pumping, it is possible to control these energy oscillations in such a way that coherence in the laser system appears below the lasing threshold. In this approach, the radiation linewidth is two orders of magnitude smaller than the linewidth of a conventional laser for the same photon number. In addition, the second order coherence function of the output radiation is reduced from two to one before the system reaches a positive population inversion. Our results pave the way for the creation of nanoscale sources of coherent radiation that can operate below the lasing threshold.

Phonon maser stimulated by spin postselection

In a sequence of single spins interacting longitudinally with a mechanical oscillator, and using the micromaser model with random injection, we show that after an appropriate post-selection of each spin, a phonon laser analog with Poisson statistics is created with nearly perfect coherence, evidenced by the second order coherence function that goes asymptotically to one. The non-linear gain of the system depends crucially on the properly post-selected spin state as well as the pump. Our model and results suggest that the mechanism of interaction followed by a post-selected state or partial trace (common in laser/maser theory) of the spins may create the coherent vibrational radiation. However, for situations where the mechanical losses are high and it is imposible to decrease these, then the heralded post-selection can be the only resource to get phonon lasing if compared to the partial trace operation. These ideas and results may be useful for further theoretical and technical developments.

Entangled nonlinear displaced number states

Entangled nonlinear displaced number states are defined as the superposition of separable two-mode nonlinear displaced number states. In this paper, the nonlinear functions related to the harmonious states and trapped ion motion in center of mass system are considered. Considering the importance of non-classical states in quantum information theory, the non-classical properties of these states, such as photon statistics and entanglement, will be studied. Photon statistics of the entangled nonlinear displaced number states is evaluated by calculating the Mandel parameter and second order coherence function; the entanglement of the states is also examined by calculating concurrence. According to calculations, all of the introduced states have sub-Poissonian photon statistics in some range of coherent amplitude where this range becomes larger by increasing the number of the photons, n. It was also observed that the quantum second-order coherence function of the maximally entangled states represent photon antibunching effect in all values of the related parameters.

Photon–photon correlations with a V-type three-level system interacting with two quantized field modes

We carry out a model study on the interaction of a $V$-type three-level emitter with two quantized cavity modes which are weakly driven by two classical fields. The emitter may be an atom or a molecule with nondegenerate upper levels in general. The lifetimes of the two upper levels are assumed to be much longer than the lifetime of the cavity photons. We calculate the two-time second order coherence function, namely Hanbury Brown-Twiss function $g^{(2)}(\tau)$ where $\tau$ is the time delay between the two modes. We analyze the photon-photon correlations between the two cavity modes in terms of $g^{(2)}(\tau)$. The variation of $g^{(2)}(\tau)$ as a function of $\tau$ exhibits collapse and revival type oscillations as well as quantum beats for relatively short $\tau$ while in the limit $\tau \rightarrow \infty$, $g^{(2)}(\tau) \simeq 1$. We further show that the two cavity field modes are entangled when $g^{(2)}(0) > 2$. We develop a dressed state picture with single photon in each mode to explain the results and use the negativity of the partial transpose of the reduced field density matrix to show the entanglement between field modes. The model presented in this paper may be useful for generating entangled photon pairs, and also manipulating photon-photon correlations with a cavity QED set up.

The Role of Dissipation in the Two–Color Second–Order Coherence Function for Light Sources

We discuss the effect of the dissipation and pump rates in the two-photon spectrum (2PS) for different light sources. In this paper we show the second-order coherence function for the different frequencies given of the systems, we show how this measure reveals more information about the light source, and we show how it changes with dissipation and pump rates. We emphasize the importance of modelling system as an open quantum system for a more realistic description of the spectrum S(ω) and 2PS of field light

Second-order coherence properties of amplified spontaneous emission from a high-power tapered superluminescent diode

We study the degree of second-order coherence of the emission of a high-power multi-quantum well superluminescent diode with a lateral tapered amplifier section with and without optical feedback. When operated in an external cavity, the degree of second-order coherence changed from the almost thermal case of towards the mostly coherent case of when the injection current at the tapered section was increased. We found good agreement with semi-classical laser theory near and below threshold while above laser threshold a slightly higher g(2)(0) was observed. As a free running device, the superluminescent diode yielded more than 400 mW of optical output power with good spatial beam quality of . In this case, the degree of second-order coherence dropped only slightly from 1.9 at low powers to 1.6 at the maximum output power. To our knowledge, this is the first investigation of a high-power tapered superluminescent diode concerning the degree of second-order coherence. Such a device might be useful for real-world applications probing the second order coherence function, such as ghost imaging.

Polarized single photon emission and photon bunching from an InGaN quantum dot on a GaN micropyramid

We report on excitonic single photon emission and biexcitonic photon bunching from an InGaN quantum dot formed on the apex of a hexagonal GaN micropyramid. An approach to suppress uncorrelated emission from the pyramid base is proposed, a metal film is demonstrated to effectively screen background emission and thereby significantly enhance the signal-to-background ratio of the quantum dot emission. As a result, the second order coherence function at zero time delay is significantly reduced (to = 0.24, raw value) for the excitonic autocorrelation at a temperature of 12 K under continuous wave excitation, and a dominating single photon emission is demonstrated to survive up to 50 K. The deterioration of the -value at elevated temperatures is well understood as the combined effect of reduced signal-to-background ratio and limited time resolution of the setup. This result underlines the great potential of site-controlled pyramidal dots as sources of fast polarized single photons.

Temporal coherence of one-dimensional nonequilibrium quantum fluids

We theoretically investigate the time dependence of the first order coherence function for a one-dimensional driven dissipative non-equilibrium condensate. Simulations on the generalized Gross-Pitaevskii equation (GGPE) show that the characteristic time scale of exponential decay agrees with the linearized Bogoliubov theory in the regime of large interaction energy. For very weak interactions, the temporal correlation deviates from the linear theory, and instead respects the dynamic scaling of the Kardar-Parisi-Zhang universality class. This nonlinear dynamics is found to be quantitatively captured by a noisy Kuramoto-Sivashinsky equation for the phase dynamics.

Electro-optical switching between polariton and cavity lasing in an InGaAs quantum well microcavity.

We report on the condensation of microcavity exciton polaritons under optical excitation in a microcavity with four embedded InGaAs quantum wells. The polariton laser is characterized by a distinct non-linearity in the input-output-characteristics, which is accompanied by a drop of the emission linewidth indicating temporal coherence and a characteristic persisting emission blueshift with increased particle density. The temporal coherence of the device at threshold is underlined by a characteristic drop of the second order coherence function to a value close to 1. Furthermore an external electric field is used to switch between polariton regime, polariton condensate and photon lasing.

Linearly polarized single photon antibunching from a site-controlled InGaN quantum dot

We report on the observation of linearly polarized single photon antibunching in the excitonic emission from a site-controlled InGaN quantum dot. The measured second order coherence function exhibits a significant dip at zero time difference, corresponding to gm2(0)=0.90 under continuous laser excitation. This relatively high value of gm2(0) is well understood by a model as the combination of short exciton life time (320 ps), limited experimental timing resolution and the presence of an uncorrelated broadband background emission from the sample. Our result provides the first rigorous evidence of InGaN quantum dot formation on hexagonal GaN pyramids, and it highlights a great potential in these dots as fast polarized single photon emitters if the background emission can be eliminated.

Polariton quantum blockade in a photonic dot

We investigate the quantum nonlinear dynamics of a resonantly excited photonic quantum dot embedding a quantum well in the strong exciton-photon coupling regime. Within a master equation approach, we study the polariton quantum blockade and the generation of single photon states due to polariton-polariton interactions as a function of the photonic dot geometry, spectral linewidths and energy detuning between quantum well exciton and confined photon mode. The second order coherence function $g^{(2)}(t,t')$ is calculated for both continuous wave and pulsed excitations.

Coherence properties of two trapped particles

We analyse the coherence properties of two particles trapped in a one-dimensional harmonic potential. This simple model allows us to derive analytic expressions for the first and second order coherence functions. We investigate their properties depending on the particle nature and the temperature of the quantum gas. We find that at zero temperature non-interacting bosons and fermions show very different correlations, while they coincide for higher temperatures. We observe atom bunching for bosons and atom anti-bunching for fermions. When the effect of s-wave scattering between bosons is taken into account, we find that the range of coherence is enhanced or reduced for repulsive or attractive potentials, respectively. Strongly repelling bosons become in some way more “fermion-like" and show anti-bunching. Their first order coherence function, however, differs from that for fermions.

Photon-photon interactions in cavity electromagnetically induced transparency

Dissipation-free photon-photon interaction at the single photon level is studied in the context of cavity electromagnetically induced transparency (EIT). For a single multilevel atom exhibiting EIT in the strong cavity-coupling regime, the anharmonicity of the atom-cavity system has an upper bound determined by single atom-photon coupling strength. Photon blockade is inferred to occur for both single and multi-atom cases from the behaviour of transition rates between dressed states of the system. Numerical calculations of the second order coherence function indicate that photon antibunching in both single and two-atom cases are strong and comparable.

Photon statistics of a bad-cavity laser near threshold

A simple model of a bad-cavity laser is presented based on Haken's master equation for N pumped two-level atoms in a cavity. Via adiabatic elimination of fast variables the whole photon statistics is solved analytically near threshold. It is shown that the second order coherence function g (2) (0) has a very different behavior near threshold for a bad-cavity laser compared to a good-cavity laser. The power spectrum illustrates nicely the different time scales involved in the dynamics.

Dynamical algebraic connection between the Stark and Kerr effects

We show that the Stark and Kerr Hamiltonians are deeply connected in the framework of dynamical algebras. We found that the algebras for both Hamiltonians are the same when physically relevant magnitudes, such as the population inversion and the $n$th order coherence function are considered as elements of a Lie algebra under commutation with the Hamiltonians. By analyzing the equations of motion we were able to find a set of conditions for the characteristic magnitudes of both Hamiltonians that leads to the same dynamical behavior for all the elements of the group. Finally, we conclude that the results of this paper can be generalized to any extension of the Jaynes-Cummings model, where any of the different elements of the group are present.

DYNAMICS OF A NONDEGENERATE TWO-PHOTON JAYNES–CUMMINGS MODEL

A generalized Jaynes–Cummings model including the Stark shifts is investigated where the transition is mediated by two different modes of photons. For two different types of correlated field states, the pair coherent states and two-mode SU(1, 1) coherent states, the effect of including the Stark shift on the dynamical behavior of atomic inversion, atomic squeezing parameters, second order coherence function, and photon number distribution is investigated. Our results indicate significant changes in the behavior of these quantities for large and small average photon number <n> in the presence and absence of Stark shift and depending on the type of correlated field involved.

SQUEEZING AND OTHER NON-CLASSICAL FEATURES IN k-PHOTON ANHARMONIC OSCILLATOR IN BINOMIAL AND NEGATIVE BINOMIAL STATES OF THE FIELD

A systematic study of squeezing obtained from k-photon anharmonic oscillator (with interaction hamiltonian of the form (a†)kak, k ≥ 2) interacting with light whose statistics can be varied from sub-Poissonian to poissonian via binomial state of field and super-Poissonian to poissonian via negative binomial state of field is presented. We predict that for all values of k there is a tendency increase in squeezing with increased sub-Poissonian character of the field while the reverse is true with super-Poissonian field. We also present non-classical behavior of the first order coherence function explicitly for k = 2 case (i.e., for two-photon anharmonic oscillator model used for a Kerr-like medium) with variation in the statistics of the input light.

Propagation of randomly perturbed pulsed plane waves in a nonlinear medium

Analytical expressions are obtained that govern the amplification of initially weak field fluctuations of a pulsed plane wave propagating in an inertially nonlinear medium. The equation for the coherence function of the second order is derived in the regime of saturated field fluctuations. An asymptotic analysis of irradiance field fluctuations at great distances of propagation is given based on the solution of this equation.