Two different regimes in a V-type three-level atom trapped in an optical cavity

In this paper two different behaviors of a V-type three-level atom which is driven by a classical field in an optical cavity are shown. We show that the behavior of an atom depends on the values of the critical photon number. The system treatment for large enough values of the critical photon number is described by the semiclassical laser theory. In contrast, for small enough values of the critical photon number, the system shows new quantum properties. In the former case, it is shown that the system performs like a conventional laser and in the latter one, the system acts as an effective two-level model. The behaviors of the system are investigated both in the semiclassical approximation and full quantum theory. For comparing the results, computer simulations are implemented.     

Intensity noise reduction of twin beams by a passive semiconductor medium

Abstract

A passive optical system is proposed to explore the intensity quantum correlation of two twin beams to reduce the photon noise of one of them. It consists of using a semiconductor medium inside an optical cavity, which behaves as a nonlinear medium presenting a crossed Kerr effect. The intensity fluctuations of one beam modify the resonance condition of the cavity for the other beam and therefore its intensity. The medium is described microscopically within the two-level atom model. It is shown that, under typical experimental conditions, this system may produce noise reduction.     

Coherence phenomena in coupled pptical resonators

Abstract

We predict a variety of photonic coherence phenomena in passive and active coupled ring resonators. Specifically, the effective dispersive and absorptive steady-state response of coupled resonators is derived, and used to determine the conditions for coupled-resonator-induced transparency and absorption, lasing without gain, and cooperative cavity emission. These effects rely on coherent photon trapping, in direct analogy with coherent population trapping phenomena in atomic systems. We also demonstrate that the coupled-mode equations are formally identical to the two-level atom Schrödinger equation in the rotating-wave approximation, and use this result for the analysis of coupled-resonator photon dynamics. Notably, because these effects are predicted directly from coupled-mode theory, they are not unique to atoms, but rather are fundamental to systems of coherently coupled resonators.     

A Solvable Model for Light Scattering in a Stationary Field

The quantum statistical properties of independent light beams are considered, forming interference fringes, which are in interaction with a particle (electron) beam treated as a two-level system. Using the master equation and the generalized Fokker-Planck equation techniques, the photocount statistics are derived and it is demonstrated that the whole, initially coherent, radiation field remains coherent for all times while single modes exhibit two-peak bistable behaviour, varying their photon statistics from Poisson statistics to some intermediate statistics for coherent and chaotic radiation.     

The nonlinear effects over time evolution of a three-level atom confined in a single mode optical cavity

A single atom is trapped in an optical cavity in the presence and absence of a nonlinear mirror corresponding to the nonlinear and linear regimes, respectively. The time evolutions of both systems are derived. The resultant equations are numerically solved by a fourth-order Runge–Kutta method. The effect of the nonlinear mirror over time evolution of the population inversion, the mean photon number and the second-order coherence function is investigated. It is shown that in the presence of the nonlinear effects, the time average of the population inversion is increased. As the time evolution proceeds, the mean photon number is decreased as well as the light exhibiting sub-Poissonian photon distributions. Under specific conditions and in a weak-driving limit, these systems can be well approximated by an effective two-level atom. The result of the calculations confirms the predictions of the two-level model.     

Determining the state of a single cavity mode from photon statistics

Abstract

We present various schemes for measuring the quantum state of a single mode of the electromagnetic field. These involve measuring the photon statistics for the mode before and after an interaction with either one or two two-level atoms. The photon statistics conditioned on the final state of the atoms, for two choices of the initial set of atomic states, along with the initial photon statistics, may be used to calculate the complete quantum state in a simple manner. Alternatively, when one atom is used, two unconditioned sets of photon statistics, each after interaction with a single atom in different initial states, along with the initial photon statistics may be used to calculate the initial state in a simple manner. When the cavity is allowed to interact with just one atom, only pure cavity states which do not contain zeros in the photon distribution may be reconstructed. When two atoms are used we may reconstruct pure states which do not contain adjacent zeros in the photon distribution. Coherent states and number states are among those that may be measured with one-atom interaction, and squeezed states and ?Schrödinger cats‘ are among those that may be measured with a two-atom interaction.     

On the possibility of preparing decoherence-free states in a cavity

The effect of decoherence in a quantum system can be viewed as a consequence of the interaction with the environment. As has been pointed out first by Dicke, in a system of N two-level atoms where each of the atoms is individually dipole coupled to the environment, there are collective subradiant states that have no dipole coupling to photon modes, and therefore they are expected to decay more slowly. We have recently proposed a scheme which is intended to create such states in a detuned cavity. We shall examine here the conditions under which our scheme can be used and compare them with the experimental possibilities. The analysis shows that our proposal can be implemented with present-day techniques achieved in atom—cavity interaction experiments.     

Field quantization,photons and non-Hermitean modes

Field quantization in unstable optical systems is treated by expanding the vector potential in terms of non-Hermitean (Fox-Li) modes. We define non-Hermitean modes and their adjoints in both the cavity and external regions and make use of the important bi-orthogonality relationships that exist within each mode set. We employ a standard canonical quantization procedure involving the introduction of generalized coordinates and momenta for the electromagnetic (EM) field. Three-dimensional systems are treated, making use of the paraxial and monochromaticity approximations for the cavity non-Hermitean modes. We show that the quantum EM field is equivalent to a set of quantum harmonic oscillators (QHOs), associated with either the cavity or the external region non-Hermitean modes, and thus confirming the validity of the photon model in unstable optical systems. Unlike in the conventional (Hermitean mode) case, the annihilation and creation operators we define for each QHO are not Hermitean adjoints. It is shown that the quantum Hamiltonian for the EM field is the sum of non-commuting cavity and external region contributions, each of which can be expressed as a sum of independent QHO Hamiltonians for each non-Hermitean mode, except that the external field Hamiltonian also includes a coupling term responsible for external non-Hermitean mode photon exchange processes. The non-commutativity of certain cavity and external region annihilation and creation operators is associated with cavity energy gain and loss processes, and may be described in terms of surface integrals involving cavity and external region non-Hermitean mode functions on the cavity-external region boundary. Using the essential states approach and the rotating wave approximation, our results are applied to the spontaneous decay of a two-level atom inside an unstable cavity. We find that atomic transitions leading to cavity non-Hermitean mode photon absorption are associated with a different coupling constant to that for transitions leading to photon emission, a feature consequent on the use of non-Hermitean mode functions. We show that under certain conditions the spontaneous decay rate is enhanced by the Petermann factor.     

Quantum Optics with One Atom in an Optical Cavity

Abstract

The quantum mechanical master equation for a single two-level atom in a single-mode optical cavity is numerically solved in both the quantum and the semiclassical limits. The quantum limit of few cavity photons shows semiclassically forbidden behaviour such as steady state two-level population inversion. Qualitatively new fluorescent spectra, having sidebands broadened by the cavity interaction, also occur. The quantum theory of the single-atom laser with injected signal is presented. At the interface between its quantum and semiclassical dynamics we elucidate the signature of semiclassical limit cycles.     

Quantum dynamics and nonclassical photon statistics of coherently driven Raman transition in bimodal cavity

We study a classically driven two-level system in a harmonic trap and a lossy two-mode cavity, with the first mode being resonant to the driving field and an electronic transition, and the second mode being off-resonant, forming a vibrational-assisted Raman transition. Using an exact numerical method, we compute the steady state as well as the time evolution of the photon statistics. We further investigate the photon correlations of both the cavity modes and identify the laser parameters and coupling strength that give the nonclassical sub-Poissonian property. The work is useful for coherent control of photon statistics and photon correlations in the trapped two-level system.     

Two-level atom and multichromatic waves in a lossless cavity

Abstract

In this paper, we shall examine a generalized version of the Jaynes-Cummings model in which a two-level atom moves in a lossless cavity and is coupled to multichromatic waves with general frequencies and coupling constants. We shall show that both the motion of the atom and the photon conversion between multichromatic waves are dynamically correlated. Using the semiclassical approximations introduced in a previous paper, we obtain the equations which describe the dynamics of this quantum system and discuss the solutions in several special cases. In particular, we point out that the motion of the atom may be controlled by the electromagnetic modes, and vice versa, that is the amplitudes and phases of the electromagnetic fields in the cavity may also be determined by the position of the atom.     

Direct measurement of photon number statistics at telecom wavelengths using a charge integration photon detector

In optical quantum information technology, a photon number resolving detector (PNRD) is the basic device for developing photonic quantum computers. The demands for the PNRD are high quantum efficiency and wide dynamic range. We have developed a charge integration photon detector (CIPD) with a quantum efficiency of 80% at telecom wavelengths. The repetition rate of the CIPD is as low as 40 Hz at present, but it can be applied for measurement of short pulses. We report the capability of the CIPD for multiphoton counting over 10 photons, its responsivity to the short pulses, and its high linearity using a binary intensity modulated short pulse (2 ns) train and simultaneous irradiation of two kinds of pulses.     

Effect of decoherence on the radiative and squeezing properties in a coherently driven trapped two-level atom

Analysis of the effects of decoherence on the radiative and squeezing properties of a coherently driven two-level atom trapped in a resonant cavity applying the corresponding master equation is presented. The atomic dynamics as well as the squeezing and statistical properties of the emitted radiation are investigated. It is found that the atom stays in the lower energy level more often at steady state irrespective of the strength of the coherent radiation and thermal fluctuations entering the cavity. Moreover, a strong external coherent radiation results in the splitting of the line of the emission spectrum, whereas the decoherence broadens the width and significantly decreases the height. It is also found that the emitted radiation exhibits photon anti-bunching, super-Poissonian photon statistics and squeezing, despite the presence of the decoherence which is expected to destroy the quantum features.     

Design of an Optical Absorption Cavity for Titanium Transition Edge Sensors

We have developed a TES optical photon detector with a titanium superconducting film showing a very fast response with rise time and fall times of 30 ns and 313 ns, respectively. The fast response is promising for many quantum measurement applications. Increasing the quantum efficiency of this device from the current value of ∼20% makes the detector even more suitable for these applications. Here we report on simulation and experimental results of a cavity designed to improve optical photon absorption of titanium.     

Optical Absorptions of Impurity-Bound Polaron in a GaAs Quantum Dot with Parabolic Potential

The linear and nonlinear optical properties considering polaron and Coulomb impurity effect in a GaAs parabolic quantum dot are investigated theoretically. Calculations have been performed by using the compact density-matrix approach and the Lee-Low-Pines-Huybrecht variational technique for all electron–LO–phonon coupling strengths. The dependence of the optical absorption coefficients on the incident photon energy, the Coulomb potential and incident optical intensity is also studied.     

Analysis of quantum noise in a singly resonant nondegenerate optical parametric oscillator

We have analyzed the evolution of quantum operators in a three-wave mixing process by using the nonlinear polarization driven wave equations and linearization of the quantum operators. We have theoretically shown that a nondegenerate optical parametric amplifier can generate amplitude-squeezed light when operated in the backconversion regime. Furthermore, a nondegenerate optical parametric oscillator, where only the signal wave is resonant, is proved to generate amplitude-squeezed light when the pump intensity is above the value at which 100% photon conversion efficiency is achieved. The calculated limit for amplitude-squeezing in this case is 3 d B.     

Parametric downconversion vs optical parametric amplification: a comparison of their quantum statistics

The extent to which the intense light generated by an unseeded, high-gain optical parametric amplifier retains the desired quantum statistical properties of the individual photon pairs generated by spontaneous parametric downconversion is analysed. It is shown that certain but not all of these properties are retained, with important implications for applications of quantum optics.     

Effective preparation of the N-dimension spin Greenberger–Horne–Zeilinger state with quantum dots embedded in microcavities

We propose a scheme for preparation of the N-dimension spin Greenberger–Horne–Zeilinger state by exploiting quantum dots (QDs) embedded in microcavities. Numerically analysed results show that with the spin-selective photon reflection from the cavity, we can complete the scheme assisted by one polarized photon with high fidelity and 100% successful probability in principle. Furthermore, the set-up is just composed of simple linear optical elements, delay lines and conventional photon detectors, which are feasible with existing experimental technology. Moreover, QDs have numerous admirable features in weak-coupling regime, which are practicable in realistic cavity quantum electrodynamics system shown by previous numerical simulations and experiments. Therefore, our scheme might be realized in near future.     

Three-pulse photon echo induced by the optical transition of excitons in core-shell CdSe/ZnS nanocrystal quantum dots

The femtosecond three-pulse photon echo phenomena induced by the optical transition of 1s_e1s_h exciton in a core-shell CdSe/ZnS nanocrystal quantum dot (NQD) are theoretically investigated basing on the optical Bloch equations. The parameter dependence of the photon echo signals is discussed. The numerical calculation results reveal that three-pulse photon echo signals are sensitive to the variation of the size and structure of NQD. The corresponding mechanism has been discussed in terms of quantum size confined effect theory.     

Fast CNOT gate via shortcuts to adiabatic passage

Based on the shortcuts to adiabatic passage, we propose a scheme for directly implementing a controlled-not (CNOT) gate in a cavity quantum electrodynamics system. Moreover, we generalize the scheme to realize a CNOT gate in two separate cavities connected by an optical fiber. The strictly numerical simulation shows that the schemes are fast and insensitive to the decoherence caused by atomic spontaneous emission and photon leakage. In addition, the schemes can provide a theoretical basis for the manipulation of the multiqubit quantum gates in distant nodes of a quantum network.