Atom Maser Research Articles

Large deviations, central limit, and dynamical phase transitions in the atom maser

The theory of quantum jump trajectories provides a new framework for understanding dynamical phase transitions in open systems. A candidate for such transitions is the atom maser, which for certain parameters exhibits strong intermittency in the atom detection counts and has a bistable stationary state. Although previous numerical results suggested that the “free energy” may not be a smooth function, we show that the atom detection counts satisfy a large deviations principle and, therefore, we deal with a phase crossover rather than a genuine phase transition. We argue, however, that the latter occurs in the limit of an infinite pumping rate. As a corollary, we obtain the central limit theorem for the counting process. The proof relies on the analysis of a certain deformed generator whose spectral bound is the limiting cumulant generating function. The latter is shown to be smooth so that a large deviations principle holds by the Gärtner–Ellis theorem. One of the main ingredients is the Krein–Rutman theory, which extends the Perron–Frobenius theorem to a general class of positive compact semigroups.

Phase locking of a semiconductor double-quantum-dot single-atom maser

We experimentally study the phase stabilization of a semiconductor double quantum dot (DQD) single atom maser by injection locking. A voltage-biased DQD serves as an electrically tunable microwave frequency gain medium. The statistics of the maser output field demonstrate that the maser can be phase locked to an external cavity drive, with a resulting phase noise of -99 dBc/Hz at a frequency offset of 1.3 MHz. The injection locking range, and the phase of the maser output relative to the injection locking input tone are in good agreement with Adler's theory. Furthermore, the electrically tunable DQD energy level structure allows us to rapidly switch the gain medium on and off, resulting in an emission spectrum that resembles a frequency comb. The free running frequency comb linewidth is ~8 kHz and can be improved to less than 1 Hz by operating the comb in the injection locked regime.

Threshold Dynamics of a Semiconductor Single Atom Maser.

We demonstrate a single atom maser consisting of a semiconductor double quantum dot (DQD) that is embedded in a high-quality-factor microwave cavity. A finite bias drives the DQD out of equilibrium, resulting in sequential single electron tunneling and masing. We develop a dynamic tuning protocol that allows us to controllably increase the time-averaged repumping rate of the DQD at a fixed level detuning, and quantitatively study the transition through the masing threshold. We further examine the crossover from incoherent to coherent emission by measuring the photon statistics across the masing transition. The observed threshold behavior is in agreement with an existing single atom maser theory when small corrections from lead emission are taken into account.

Simulation of Nikola Tesla Atmospheric (Maser) Discharges

In this paper, an attempt is made in the laboratory to simulate Nikola Tesla atmospheric maser discharges. The ground lightning bolt, commonly observed, takes the form of filamentary lightning channels called the leader and the return strokes. It is taken that Nikola Tesla atmospheric discharges are obtained when a powerful high-frequency source triggers the atmospheric discharge and enables the energy stored in the cumulonimbus clouds to be released in the form of maser radiations, which are accompanied by a diffuse glow-like discharge covering a large area, as in the case of the aurora borealis. The main point in the current investigation is the generation of the powerful hydrogen atom (maser) line at 1.420 GHz recorded under the condition of high humidity present in air. This suggests that the driving frequency of high power at a frequency close to 1 GHz is capable of electrolysis of the water vapor present in air, dissociation of the hydrogen molecule into atoms, excitation of atomic hydrogen, and consequent emission from the hydrogen atoms in the manner found in the hydrogen atomic clock.

Fisher informations and local asymptotic normality for continuous-time quantum Markov processes

We consider the problem of estimating an arbitrary dynamical parameter of an open quantum system in the input–output formalism. For irreducible Markov processes, we show that in the limit of large times the system-output state can be approximated by a quantum Gaussian state whose mean is proportional to the unknown parameter. This approximation holds locally in a neighbourhood of size in the parameter space, and provides an explicit expression of the asymptotic quantum Fisher information in terms of the Markov generator. Furthermore we show that additive statistics of the counting and homodyne measurements also satisfy local asymptotic normality and we compute the corresponding classical Fisher informations. The general theory is illustrated with the examples of a two-level system and the atom maser. Our results contribute towards a better understanding of the statistical and probabilistic properties of the output process, with relevance for quantum control engineering, and the theory of non-equilibrium quantum open systems.

Lasing in circuit quantum electrodynamics with strong noise

A single artificial atom maser can be realized using a superconducting single electron transistor coupled to an oscillator or a double dot coupled to a transmission-line resonator. The authors suggest a model to describe the possibility of lasing action in various environments under different coupling mechanism.

Maximum likelihood versus likelihood-free quantum system identification in the atom maser

We consider the problem of estimating a dynamical parameter of a Markovian quantum open system (the atom maser), by performing continuous time measurements in the systemʼs output (outgoing atoms). Two estimation methods are investigated and compared. Firstly, the maximum likelihood estimator (MLE) takes into account the full measurement data and is asymptotically optimal in terms of its mean square error. Secondly, the ‘likelihood-free’ method of approximate Bayesian computation (ABC) produces an approximation of the posterior distribution for a given set of summary statistics, by sampling trajectories at different parameter values and comparing them with the measurement data via chosen statistics. Building on previous results which showed that atom counts are poor statistics for certain values of the Rabi angle, we apply MLE to the full measurement data and estimate its Fisher information. We then select several correlation statistics such as waiting times, distribution of successive identical detections, and use them as input of the ABC algorithm. The resulting posterior distribution follows closely the data likelihood, showing that the selected statistics capture ‘most’ statistical information about the Rabi angle.

Asymptotic inference in system identification for the atom maser

System identification is closely related to control theory and plays an increasing role in quantum engineering. In the quantum set-up, system identification is usually equated to process tomography, i.e. estimating a channel by probing it repeatedly with different input states. However, for quantum dynamical systems such as quantum Markov processes, it is more natural to consider the estimation based on continuous measurements of the output, with a given input that may be stationary. We address this problem using asymptotic statistics tools, for the specific example of estimating the Rabi frequency of an atom maser. We compute the Fisher information of different measurement processes as well as the quantum Fisher information of the atom maser, and establish the local asymptotic normality of these statistical models. The statistical notions can be expressed in terms of spectral properties of certain deformed Markov generators, and the connection to large deviations is briefly discussed.

Quantum trajectory phase transitions in the micromaser

We study the dynamics of the single-atom maser, or micromaser, by means of the recently introduced method of thermodynamics of quantum jump trajectories. We find that the dynamics of the micromaser displays multiple space-time phase transitions, i.e., phase transitions in ensembles of quantum jump trajectories. This rich dynamical phase structure becomes apparent when trajectories are classified by dynamical observables that quantify dynamical activity, such as the number of atoms that have changed state while traversing the cavity. The space-time transitions can be either first order or continuous, and are controlled not just by standard parameters of the micromaser but also by nonequilibrium "counting" fields. We discuss how the dynamical phase behavior relates to the better known stationary-state properties of the micromaser.

Atomic detection in microwave cavity experiments: A dynamical model

We construct a model for the detection of one atom maser in the context of cavity Quantum Electrodynamics (QED) used to study coherence properties of superpositions of electromagnetic modes. Analytic expressions for the atomic ionization are obtained, considering the imperfections of the measurement process due to the probabilistic nature of the interactions between the ionization field and the atoms. Limited efficiency and false counting rates are considered in a dynamical context, and consequent results on the information about the state of the cavity modes are obtained.

Structural Hamiltonian chaos in the coherent parametric atom–field interaction

We consider one of the simplest semiclassical models in laser and atomic physics, a collection of two-level atoms interacting coherently with an electromagnetic standing wave in an ideal single-mode cavity within the rotating-wave approximation (RWA). In the strong-coupling limit, atoms and a cavity field constitute a strongly coupled atom–field dynamical system whose atomic and field variables oscillate in a self-consistent way with the Rabi frequency. It is proven analytically by the Melnikov method and numerically by computing maximal Lyapunov exponents and Poincaré sections that the parametric Rabi oscillations in a vibrating cavity may be chaotic in a sense of exponential sensitivity to initial conditions. Wavelet spectra computed with typical signals of the oscillations demonstrate clearly that Hamiltonian chaos in the coherent atom–field interaction with modulated coupling is structural. Structural chaos is characterized by positive values of the maximal Lyapunov exponents and regular structures which coexist in the same signal. Duration of a train of regular oscillations is defined by the period of modulation, but oscillations between successive trains are chaotic. Results of numerical experiments and estimation of the control parameters and approximations involved show that a Rydberg atom maser operating with a collection of two-level atoms inside a high-quality superconducting microwave cavity is a promising device for observing manifestations of structural Hamiltonian chaos in real experiments.

Theory of the coherent population trapping maser: A strong-field self-consistent approach

The phenomenon of coherent microwave stimulated emission in a cavity is analyzed for the case of alkali atoms such as Cs and Rb under coherent population trapping (CPT) in a \ensuremath{\Lambda} scheme. The calculations are made in transient and in continuous operation within the framework of a three level model. The coupling of the atoms to the microwave field generated inside the cavity by the atomic ensemble, is fully taken into account; it introduces radiation damping and an imbalance in the populations of the ground-state hyperfine levels, decreasing the intrinsic symmetry of the \ensuremath{\Lambda} scheme. The effect leads also to a broadening and to a frequency shift of the microwave emission profile. A comparison is made with the optically pumped alkali atom maser, allowing a deeper understanding of the CPT stimulated emission phenomenon.

Structural chaos in reversible spontaneous emission of moving atoms

t is proved analytically and numerically that, under certain conditions, the reversible spontaneous emission of two-level atoms moving in a high-Q resonator and described quantum-classically can be chaotic in the sense of the exponential sensitivity with respect to the initial conditions. The wavelet analysis of the vacuum Rabi oscillations showed that this chaos is structural. The numerical estimates showed that a Rydberg atom maser with a superconducting microwave resonator operating in a strong coupling mode is a promising device for detecting mani-festations of the dynamic chaos in the reversible spontaneous emission.

Entanglement and superposition states in the micromaser

In this paper recent experiments with the one–atom maser or micromaser are reviewed. They deal with the dynamical behavior of the field at parameter values where the field undergoes phase transitions. Furthermore, atomic interferences are observed in the micromaser when the inversion of the atoms leaving the cavity is measured while the cavity frequency is scanned across the atomic resonance. The interferences are due to the non–adiabatic mixing of dressed states at the entrance and exit holes of the maser cavity. The interference structures are triangular shaped and approximately equidistant. They are associated with the dynamics of the atom–field interaction, show quantum jumps and demonstrate bistability of the micromaser field.

Photon statistics and quantum fluctuation in the two-photon Jaynes-Cummings model

The evolution of initial coherent and squeezed states in the two-photon Jaynes-Cummings model has been studied. The photon distribution and quantum fluctuations of the field still change greatly in the collapse region. The quantum fluctuation can be squeezed for both the initial coherent and squeezed states. In a short-time region, there is a limitation on the squeezing. Deeper squeezing can be reached for a larger initial photon number. It is predicted that the Rydberg atom maser can produce a squeezed state maser output.

The two-photon Rydberg atom micromaser

A Rydberg atom maser operated on a two-photon degenerate atomic transition is discussed. This device combines two interesting features: it is a quantum oscillator working on an intrinsically nonlinear effect and it is a micromaser, with only a few atoms and a few tens of photons at a time in the cavity. The reasons why Rydberg atom-superconducting cavity systems are well adapted for two-photon maser studies are discussed, and the main properties of the device are analyzed by comparing it to Rydberg masers operating on one-photon transitions. >

1/N expansion of the statistical properties of the N Rydberg atoms maser: Application to squeezing

We give a 1/ N expansion of the quatum evolution of the N Rydberg atom maser. We show that the dominant terms coincide with the usual semi-classical approach in terms of Bloch vector. We then derive the first quantum corrections. We predict impressive values for the squeezing and sub-Poissonian statistics of the maser field.

Squeezing in a Rydberg atom maser: effect of damping and thermal field

The 1/ N expansion of the quantum evolution of the N-Rydberg atom maser is extended to include losses and thermal field effects. Small values for squeezing and subpoissonian statistics for the field are obtained for experimentally realistic Q-values and temperatures.

Squeezing in a Rydberg atom maser.

We show theoretically that a Rydberg atom maser produces during its evolution a squeezed field with sub-Poissonian statistics. We give a semiclassical interpretation of this effect.

RYDBERG ATOMS AND RADIATION IN A RESONANT CAVITY II. EXPERIMENTS

We present various experiments involving atoms interacting with resonant microwave electromagnetic fields inside a cavity, allowing to check different features of the theory presented in the previous paper. We first describe experiments about superradiant emission by states in the cavity, also called transient atoms maser; the evolution of the system is detected either on the populations by selective field ionization technique or on the microwave field itself by heterodyne detection. Very low thresholds, down to 100 atoms, for the maser emission have been observed. We then describe various aspects of collective absorption of radiation by very excited atoms including the observation of Rabi nutation in a small applied resonant field, the study of the quantum efficiency of this set-up considered as a microwave photon counter, and finally the unexpected characteristics of the blackbody radiation absorption in the cavity. In this second paper, we present various experiments on states interacting with resonant millimetric electromagnetic waves inside a cavity. These experiments show various interesting physical effects calculated in the previous paper and provide a test for the theoretical models. In a first paragraph, we will describe the experimental techniques which are common to all the experiments that will be presented afterwards. We will devote the second paragraph to an experimental study of the different characteristics of the collective atom transient emission in the cavity (the Rydberg atom maser). In the last paragraph, we will describe several experiments involving the absorption of radiation by very excited states in the cavity and showing the collective behaviour of the atoms in this absorption process. 1. Experimental techniques 1.1. P£ep_ar.ation_of_the_p_hy_sicaX_sy_stem In order to prepare the physical system which has been theoretically studied in the previous paper, i.e. a set of 2-level atoms in resonant interaction with an electromagnetic mode inside a cavity, we use the experimental set-up which Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1982221