One-atom Laser Research Articles

Time-ordering effects in a one-atom laser based on electromagnetically induced transparency

The one-atom laser based on electromagnetically induced transparency, suggested recently [Phys. Rev. Lett. 124, 093603 (2020)PRLTAO0031-900710.1103/PhysRevLett.124.093603], is capable of generating Schrödinger cat states in the regime of strong ground-state coupling. In this regime, we find the exact solution for the Schrödinger equation with a time-dependent effective Hamiltonian by considering the Magnus expansion of the time-ordered exponential and calculating analytically the time-ordering terms, omitted in the previous study. We show that the time-ordering term affects the relative phase of two coherent components of the generated Schrödinger cat state. We show this influence by calculating various nonclassicality indicators for the cavity field, such as total noise, average parity, and relative total noise. We find that time-ordering becomes important at the average photon number in the cavity below 1, in striking contrast to the case of single-pass parametric downconversion, where it becomes important at average photon number in one optical mode above 4.

Photonic tunneling effect between two coupled single-atom laser cavities imbedded within a photonic-crystal platform

In this paper we investigate the photonic tunneling effect between two coupled one-atom laser cavities. The physical system consists of two coupled photonic crystal microcavities and each cavity contains a coherently pumped two-level atom. The dynamics of the system can be described by the master equation in terms of the reduced density operator. It is shown that the photonic tunneling behavior depends on certain physical conditions of the system. In the absence of the pumping field and without dissipations, the coherent photon number imbalance between two cavities exhibits the alternating-current Josephson effect. However, when the pumping effect and losses of the system are taken into account, the mean photon number imbalance displays a damped oscillation. In addition, the influence of tunneling amplitude and photonic band-gap structure on the oscillations is also studied. The research gives a further insight into the correlated dynamics of two coupled one-atom laser systems and provides an idea for constructing novel photon tunnel devises.

Coherence and statistics of a one-atom laser in a photonic crystal microcavity

Through calculating the quantum degree of second-order coherence and photon number distribution numerically, we investigate the coherence and statistics of a one-atom laser where a coherently driven two-level atom is coupled to a photonic crystal microcavity. By going beyond the previous theoretical studies, we show that in the presence of non-secular terms the cavity field displays a variable degree of second-order coherence as a function of discontinuities in the photonic density of states. The cavity field is characterized by photon antibunching and sub-Poissonian statistics for large discontinuities. In the case of a vanishing photonic density of states on the lower Mollow sideband, we can obtain only weak antibunching. If the jump in the photonic density of states is small, the bunching and super-Poissonian statistics field is generated in the cavity. Consequently, the cavity field exhibits certain non-classical features when non-secular interaction is included into the dynamics of the system. The theoretical analysis and numerical calculations presented here coincide with recent experimental observations.

Controllable optical bistability in photonic-crystal one-atom laser

We investigate the property of optical bistability in a photonic-crystal one-atom laser when nonlinear microcavity is present. The physical system consists of a coherently driven two-level light emitter strongly coupled to a high-quality microcavity which is embedded within a photonic crystal and another coherent probing field which has incident into the microcavity. In our case, the microcavity is fabricated by nonlinear material and placed as an impurity in photonic crystal. This study reveals that such a system can exhibit optical bistability. The dependence of threshold value and hysteresis loop on the photonic band gap of the photonic crystal, driving field Rabi frequency and dephasing processes, are studied. Our results clearly illustrate the ability to control optical bistability through suitable photonic-crystal architectures and external coherent driving field, and this study suggests that in a photonic-crystal nonlinear microcavity, the one-atom laser acts as an effective controllable bistable device in the design of all-light digital computing systems in the near future.

Active optical clock

This article presents the principles and techniques of active optical clock, a special laser combining the laser physics of one-atom laser, bad-cavity gas laser, super-cavity stabilized laser and optical atomic clock together. As a simple example, an active optical clock based on thermal strontium atomic beam shows a quantum-limited linewidth of 0.51 Hz, which is insensitive to laser cavity-length noise, and may surpass the recorded narrowest 6.7 Hz of Hg ion optical clock and 1.5 Hz of very recent optical lattice clock. The estimated 0.1 Hz one-second instability and 0.27 Hz uncertainty are limited only by the relativistic Doppler effect, and can be improved by cold atoms.

Laserlike and atomlike regimes in a one-atom laser

We consider a three-level model of a one-atom laser, and show that there are two limiting regimes of parameter space, one in which the system behaves like a conventional laser and one in which the system exhibits novel quantum properties. We show that in the first limiting regime, the model can be approximated by semiclassical laser theory, and in the second limiting regime the model can be approximated as an effective two-level atom. We also perform numerical simulations that confirm the limiting behaviors predicted by these approximate descriptions.

Nonclassical light generation by a photonic-crystal one-atom laser

We investigate the effects of sub-Poissonian photon statistics and photon antibunching in the light generation by a photonic-crystal one-atom laser. The physical system consists of a two-level light emitter strongly coupled to a high-quality microcavity engineered within a photonic crystal and coherently driven by a strong external laser field. This study reveals that the electromagnetic environment provided by the photonic crystal facilitates light generation characterized by pronounced sub-Poissonian photon statistics and photon antibunching, and strongly enhanced relative to that from a one-atom laser in a conventional optical cavity. The characteristics of the cavity photon statistics are fundamentally distinct from those of a corresponding microcavity in ordinary vacuum. For large discontinuities in the photon density of states between Mollow spectral components of atomic resonance fluorescence, in the good cavity regime, the photon statistics is sub-Poissonian, in contrast to the case of a conventional cavity where sub-Poissonian photon statistics is present only for a bad cavity. These results suggest the possibility of using a photonic-crystal one-atom laser as an efficient source of nonclassical light.

Fluorescence spectrum of a one-atom laser in the strong-coupling regime

The multicomponent spectrum of the resonance fluorescence is studied based on the expansion of the Green function with respect to the coherent states for a one-atom laser. An analytical solution is derived for the spectrum in the frequency range corresponding to the vacuum Rabi oscillations in the approximation of the strong atom-field coupling and a low incoherent pump intensity.

Strongly driven one-atom laser and decoherence monitoring

We propose the implementation of a strongly driven one-atom laser, based on the off-resonant interaction of a three-level atom in $\ensuremath{\Lambda}$ configuration with a single cavity mode and three laser fields. We show that the system can be described equivalently by a two-level atom resonantly coupled to the cavity and driven by a strong effective coherent field. The effective dynamics can be solved exactly, including a thermal field bath, allowing an analytical description of field statistics and entanglement properties. We also show the possible generation of quantum superposition (Schr\"odinger cat) states for the whole atom-field system and for the field alone after atomic measurement. We propose a way to monitor the system decoherence by measuring atomic populations. Finally, we confirm the validity of our model through numerical solutions.

Auto-and cross-correlation functions of a one-atom laser in a regime of strong coupling

The spectral properties of an incoherently pumped one-atom laser operating in a regime of strong coupling are studied. The spectrum of the field outgoing from the cavity, the spectrum of resonance fluorescence of an atom, and the spectrum of the atom—field cross-correlation function are numerically calculated. Relations between the parameters of the system for which spectral lines corresponding to eigenstates of the Jaynes—Cummings Hamiltonian are resolved are found. A method for determining the widths of resonances from the spectrum of the atom—field cross-correlation function is proposed, and a procedure for measuring this function using spectroscopy of intensity fluctuations is described.

Spectrum of a one-atom laser in photonic crystals

The emission spectrum of a single-emitter laser in a photonic crystal is presented. We consider a coherently pumped two-level emitter strongly coupled to a high-quality microcavity engineered within a photonic crystal. We show that the cavity spectrum consists of both elastic and inelastic components, for which we derive analytical expressions. Our study reveals enhanced, spectrally narrower emission resulting from the radiation reservoir of the photonic crystal. The cavity field spectral characteristics are fundamentally distinct from those of a corresponding microcavity in ordinary vacuum. At high pump intensities and for large discontinuities in the photon density of states between Mollow spectral components of atomic resonance fluorescence, the emitted intensity originating from the elastic spectral component increases with the intensity of the pump and the elastic component dominates the spectrum. In the case of a vanishing photon density of states in the spectral range surrounding the lower Mollow sideband and no dipolar dephasing, the cavity spectrum is elastic.

Comparison of theory and experiment for a one-atom laser in a regime of strong coupling

Our recent paper reports the experimental realization of a one-atom laser in a regime of strong coupling (Ref. [1]). Here we provide the supporting theoretical analysis relevant to the operating regime of our experiment. By way of a simplified four-state model, we investigate the passage from the domain of conventional laser theory into the regime of strong coupling for a single intracavity atom pumped by coherent external fields. The four-state model is also employed to exhibit the vacuum-Rabi splitting and to calculate the optical spectrum. We next extend this model to incorporate the relevant Zeeman hyperfine states as well as a simple description of the pumping processes in the presence of polarization gradients and atomic motion. This extended model is employed to make quantitative comparisons with the measurements of Ref. [1] for the intracavity photon number versus pump strength and for the photon statistics as expressed by the intensity correlation function g2(tau).

Theory of a one-atom laser in a photonic band-gap microchip

We present a quantum theory of a coherently pumped two-level atom in a photonic band gap (PBG), coupled to both a multimode waveguide channel and a high-quality microcavity embedded within a photonic crystal. One mode is engineered to exhibit a sharp cutoff within the PBG, leading to a large discontinuity in the local photon density of states near the atom, and the cavity field mode is resonant with the central component of the Mollow spectrum of atomic resonance fluorescence. Another mode of the waveguide channel is used to propagate the pump beam. We derive analytical expressions for the optical amplitude, intensity, second-order correlation functions, and conjugate quadrature variances for the light emitted by the atom into the microcavity. The quantum degree of second-order coherence in the cavity field reveals enhanced, inversionless, nearly coherent light generation when the photon density of states jump between the Mollow spectral components is large. The cavity field characteristics are highly distinct from that of a corresponding high-$Q$ cavity in ordinary vacuum. In the case of a vanishing photon density of states on the lower Mollow sideband and no dipolar dephasing, the emitted photon statistics is Poissonian, and the cavity field exhibits quadrature coherence.

Experimental realization of a one-atom laser in the regime of strong coupling.

Conventional lasers (from table-top systems to microscopic devices) typically operate in the so-called weak-coupling regime, involving large numbers of atoms and photons; individual quanta have a negligible impact on the system dynamics. However, this is no longer the case when the system approaches the regime of strong coupling for which the number of atoms and photons can become quite small. Indeed, the lasing properties of a single atom in a resonant cavity have been extensively investigated theoretically. Here we report the experimental realization of a one-atom laser operated in the regime of strong coupling. We exploit recent advances in cavity quantum electrodynamics that allow one atom to be isolated in an optical cavity in a regime for which one photon is sufficient to saturate the atomic transition. The observed characteristics of the atom-cavity system are qualitatively different from those of the familiar many-atom case. Specifically, our measurements of the intracavity photon number versus pump intensity indicate that there is no threshold for lasing, and we infer that the output flux from the cavity mode exceeds that from atomic fluorescence by more than tenfold. Observations of the second-order intensity correlation function demonstrate that our one-atom laser generates manifestly quantum (nonclassical) light, typified by photon anti-bunching and sub-poissonian photon statistics.

Quantum interference effects in a cavity QED system

We consider the effect of quantum interference on population distribution and photon statistics of a cavity field interacting with dressed states of a strongly driven three-level atom. We analyse three coupling configurations of the cavity field to the driven atom, with the cavity frequency tuned to the outer Rabi sideband, the inner Rabi sideband and the central frequency of the 'singly dressed' three-level atom. The quantum doubly dressed states for each configuration are identified and the population distribution and photon statistics are interpreted in terms of transitions among these dressed states and their populations. We find that the population distribution depends strongly on quantum interference and the cavity damping. For the cavity field tuned to the outer or inner Rabi sidebands the cavity damping induces transitions between the dressed states which are forbidden for the ordinary spontaneous emission. Moreover, we find that in the case of the cavity field coupled to the inner Rabi sideband the population distribution is almost Poissonian with a large average number of photons that can be controlled by quantum interference. This system can be considered as a one-atom dressed-state laser with controlled intensity.

Quantum statistical properties of one-atom lasers

Properties of a laser formed by a high-Q cavity and a single incoherently excited atom are studied on the basis of analytical solutions obtained for the quasi-probability P-function. Expressions for the boundaries separating various operating regimes of a one-atom laser (below threshold, above threshold, and self-quenching) are found. It is shown that lasing without inversion and lasing with the decay rate of the excited state exceeding the pump intensity are possible in the system. The degree of coherence of laser radiation is studied.

Single-atom laser based on multiphoton resonances at far-off resonance in the Jaynes-Cummings ladder

We propose a scheme of a one-atom laser which produces a cavity-field virtually in a stationary Fock state. It is based upon the unexpectedly simple dynamics of the Jaynes-Cummings system at multiphoton resonances at far-off resonance. We find that an anomalously high cavity mode excitation occurs at a particular set of atomic, cavity, and driving-field frequencies.

Spectral properties of the one-atom laser

The spectral properties of a two-level one-atom laser are investigated in a systematic way below and above threshold. For strong atom-field coupling several different regimes, depending on the pump rate, can be distinguished. The quantum properties of the one-atom laser lead to multipeaked output and fluorescence spectra.

Relation between the N-atom laser and the one-atom laser.

The interaction of a quantized field mode with N identical atoms coupled to individual reserviors and classical driving fields is studied. An effective time-evolution operator for the radiation mode is derived. The exponent of this operator can be written as the number of atoms times an infinite sum containing field operators and correlation functions of freely evolving (no atom-field coupling) single-atom operators. In the adiabatic limit of fast decaying atomic correlations one can derive a master equation for the field density matrix. It is shown that the Liouvillian describing the interaction of the field mode with the N atoms is N times the single-atom Liouvillian.

Photon Statistics of the Three-level One-atom Laser

Abstract We investigate the transient and the steady-state behaviour of the photon statistics of a single-atom laser, consisting of a three-level Λ system, driven by an incoherent external pump field and strongly coupled to a single mode of an optical cavity. For several limiting cases we are able to obtain analytical results. A comparison with standard multi-atom laser theory reveals a surprisingly good agreement down to very small intracavity photon numbers. Under appropriate operating conditions a calculation of the second-order intensity correlation function yields sub-Poissonian statistics as well as strong antibunching induced by the nonlinear dynamics of the atom.