Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review Letters

Trapping States in the Micromaser

M. Weidinger, Benjamin T. H. Varcoe, R. Heerlein, HERBERT WALTHER

Published May 10, 1999• 251 citations
Publisher

Abstract

Trapping states in the one-atom maser or micromaser are predicted by maser theory and are a direct consequence of the quantization of the electromagnetic field. They have been found in our experiment when the inversion of atoms leaving the cavity is observed while the interaction time is scanned. They correspond to quantum states of the atom-cavity system and under certain conditions represent Fock states. The trapping states occur when the atom-field dynamics complete a full evolution (or multiples thereof). Owing to feedback through the maser dynamics, a stabilization of the photon number in the steady state field of the maser cavity is achieved.

DOI
10.1103/physrevlett.82.3795

Related papers

Entanglement and superposition states in the micromaser

HERBERT WALTHER

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.

Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences•Dec 15, 1997•1 citation

Generation of Fock states in the micromaser

Benjamin T. H. Varcoe, S. Brattke, HERBERT WALTHER

Summary form only given. We report on the first generation of Fock states using the micromaser. In order to produce the field, a flux of excited state atoms is passed through the cavity. The Fock states are realized in two ways: firstly in the steady state by using the trapping condition of the maser field, and secondly using state reduction of the pumping atoms. In the second experiment the purity of the Fock state could be investigated in detail by sending an additional probe atom into the cavity and investigating the dynamics of the photon exchange.

Conference on Lasers and Electro-Optics•Aug 29, 2005•0 citations

Fock State Rabi Oscillations; A Building Block for the Observation of New Phenomena in Quantum Optics

Benjamin T. H. Varcoe, S. Brattke, Berthold‐Georg Englert +1 more

In recent experiments it was demonstrated that number or Fock states of the one-atom maser can be generated. Two types of experiments have been performed. In the first one the Fock states are achieved in steady state via the so-called trapping states of the micromaser field. In the second experiment the number states were generated in a dynamical experiment by state reduction. In the latter case the generated field was afterwards probed by observing the dynamics of a probe atom in the field. The fact that Fock states of the micromaser field can be realised leads to new applications of the micromaser one of them is the generation of a many particle entanglement of the GHZ type.

Fortschritte der Physik•May 1, 2000•8 citations

Theory of the micromaser

Marlan O. Scully, Muhammad Suhail Zubairy

The development of a single-atom maser or a micromaser allows a detailed study of the atom–field interaction. The situation realized is very close to the ideal case of a single two-level atom interacting with a single-mode quantized field as treated in Section 6.2. In a micromaser a stream of two-level atoms is injected into a superconducting cavity with a high quality factor. The injection rate can be such that only one atom is present inside the resonator at any time. Due to the high quality factor of the cavity, the radiation decay time is much larger than the characteristic time of the atom–field interaction, which is given by the inverse of the single-photon Rabi frequency. Therefore, a field is built up inside the cavity when the mean time between the atoms injected into the cavity is shorter than the cavity decay time. A micromaser, therefore, allows sustained oscillations with less than one atom on the average in the cavity. The realization of a single-atom maser or a micromaser has been made possible due to the enormous progress in the construction of superconducting cavities together with the laser preparation of highly excited atoms called Rydberg atoms. The quality factor of the superconducting cavities is high enough for periodic energy exchanges between atom and cavity field to be observed. The interesting properties of the Rydberg atoms make them ideal for micromasers. In Rydberg atoms the probability of induced transitions between adjacent states becomes very large and scales as n 4 , where n denotes the principle quantum number.

Cambridge University Press eBooks•Sep 4, 1997•1 citation

Experiments with the One-atom-maser

Linas Urbonas

There are only fistful of systems in physics that can be described by an exact theory from first principles and, at the same time, can be investigated under experimental conditions approaching the idealized theoretical ones. The one-atom-maser or micromaser provides such an example, making a detailed study of the fundamental properties of the atom-field interaction possible. The situation realized in a micromaser is very close to the ideal case of a single two-level atom interacting with a single quantized mode of a cavity field. In the micromaser the atoms have a dual purpose of both pumping the field and also probing it via measurements of the outgoing atoms. Any other means of measuring the field inside the resonator has the detrimental effect of lowering its Q-factor and thereby the photon storage time. The long photon storage time of the resonator allows for the decay of the field to be negligible during the passage of an atom and its interaction with the field. The behavior of atoms in a cavity is governed by the oscillatory exchange of energy between the atoms and the field, which is called Rabi oscillation. For cavity fields in the vacuum and few photon number states (Fock states), Rabi oscillations have been measured in the past. To prevent thermal effects from polluting the pure number states these experiments were performed at low temperatures (below 1 K). However, the observed resolution of the Rabi oscillations measurements was quite disappointing (only about 2% of the predicted theoretical value) and precluded more ambitious experiments like atom-atom correlations or time resolved investigations of the maser field dynamics. The observed contrast of Rabi oscillations can be considered as a figure of merit for the experimental resolution of quantum features of a maser field. Therefore, a high resolution in the measurements of Rabi oscillations is crucial. This thesis describes the methods and improvements applied to enhance the resolution of Rabi oscillations by a factor of 8. The following upgrades and developments proved to be crucial in this work: 1) The base temperature of the cryogenic system was lowered to 0.3 K, i.e. one third of the original value. At the same time, the time during which the system remains at the base temperature was improved by almost of an order of magnitude (to more than 12 h). 2) For the promotion of the atoms to the Rydberg regime new three-step diode laser setup was constructed. The excitation efficiency compared to the old dye laser was increased by two orders. Using top-of-fringe stabilization with new spectroscopic methods, specially designed error detection and feedback schemes as well as state-of-the-art PID regulators the continuous locking of lasers is about 8 h (compared to about 20 min with the old dye laser system). 3) The flexibility of using the three step excitation allows to excite different maser states and for the first time to investigate pure maser transition. 4) Various improvements on the atomic oven and the channeltron detection unit led to the reliable and stable production and detection of the atomic beam. Observed distribution of the atomic beam statistics reaches to within 6% the Poisson limit which is expected in the absence of experimental imperfections. 5) New developed techniques in magnetic field compensation allow to perform such measurements with two orders of magnitude better accuracy compared to the previous experiments. To demonstrate the new capabilities of the apparatus and to apply its improved resolution of quantum fields we performed a previously impossible in-depth analysis of mean photon number and the atomic inversion produced by a micromaser for various detunings between the cavity- and atomic resonance frequency.

•Jan 1, 2009•0 citations

Generation of Fock states in the micromaser

Benjamin T. H. Varcoe, S. Brattke, HERBERT WALTHER

The recent observation of trapping states in the micromaser not only gave strong indications that the cavity field was quantized but also that the field was held in a number state or Fock state for long periods of time. We extend this measurement to show that under achievable experimental conditions, steady-state Fock generation is possible. Additionally, we show how the cavity field can be projected onto a number state using state reduction and then probed to determine the field state.

Journal of Optics B Quantum and Semiclassical Optics•Apr 1, 2000•24 citations
Trapping states in the one-atom maser or micromaser are predicted by maser theory and are a direct consequence of the quantization of the electromagnetic field. They have been found in our experiment when the inversion of atoms leaving the cavity is observed while the interaction time is scanned. They correspond to quantum states of the atom-cavity system and under certain conditions represent Fock states. The trapping states occur when the atom-field dynamics complete a full evolution (or multiples thereof). Owing to feedback through the maser dynamics, a stabilization of the photon number in the steady state field of the maser cavity is achieved.
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.
Summary form only given. We report on the first generation of Fock states using the micromaser. In order to produce the field, a flux of excited state atoms is passed through the cavity. The Fock states are realized in two ways: firstly in the steady state by using the trapping condition of the maser field, and secondly using state reduction of the pumping atoms. In the second experiment the purity of the Fock state could be investigated in detail by sending an additional probe atom into the cavity and investigating the dynamics of the photon exchange.
In recent experiments it was demonstrated that number or Fock states of the one-atom maser can be generated. Two types of experiments have been performed. In the first one the Fock states are achieved in steady state via the so-called trapping states of the micromaser field. In the second experiment the number states were generated in a dynamical experiment by state reduction. In the latter case the generated field was afterwards probed by observing the dynamics of a probe atom in the field. The fact that Fock states of the micromaser field can be realised leads to new applications of the micromaser one of them is the generation of a many particle entanglement of the GHZ type.
The development of a single-atom maser or a micromaser allows a detailed study of the atom–field interaction. The situation realized is very close to the ideal case of a single two-level atom interacting with a single-mode quantized field as treated in Section 6.2. In a micromaser a stream of two-level atoms is injected into a superconducting cavity with a high quality factor. The injection rate can be such that only one atom is present inside the resonator at any time. Due to the high quality factor of the cavity, the radiation decay time is much larger than the characteristic time of the atom–field interaction, which is given by the inverse of the single-photon Rabi frequency. Therefore, a field is built up inside the cavity when the mean time between the atoms injected into the cavity is shorter than the cavity decay time. A micromaser, therefore, allows sustained oscillations with less than one atom on the average in the cavity. The realization of a single-atom maser or a micromaser has been made possible due to the enormous progress in the construction of superconducting cavities together with the laser preparation of highly excited atoms called Rydberg atoms. The quality factor of the superconducting cavities is high enough for periodic energy exchanges between atom and cavity field to be observed. The interesting properties of the Rydberg atoms make them ideal for micromasers. In Rydberg atoms the probability of induced transitions between adjacent states becomes very large and scales as n 4 , where n denotes the principle quantum number.
There are only fistful of systems in physics that can be described by an exact theory from first principles and, at the same time, can be investigated under experimental conditions approaching the idealized theoretical ones. The one-atom-maser or micromaser provides such an example, making a detailed study of the fundamental properties of the atom-field interaction possible. The situation realized in a micromaser is very close to the ideal case of a single two-level atom interacting with a single quantized mode of a cavity field. In the micromaser the atoms have a dual purpose of both pumping the field and also probing it via measurements of the outgoing atoms. Any other means of measuring the field inside the resonator has the detrimental effect of lowering its Q-factor and thereby the photon storage time. The long photon storage time of the resonator allows for the decay of the field to be negligible during the passage of an atom and its interaction with the field. The behavior of atoms in a cavity is governed by the oscillatory exchange of energy between the atoms and the field, which is called Rabi oscillation. For cavity fields in the vacuum and few photon number states (Fock states), Rabi oscillations have been measured in the past. To prevent thermal effects from polluting the pure number states these experiments were performed at low temperatures (below 1 K). However, the observed resolution of the Rabi oscillations measurements was quite disappointing (only about 2% of the predicted theoretical value) and precluded more ambitious experiments like atom-atom correlations or time resolved investigations of the maser field dynamics. The observed contrast of Rabi oscillations can be considered as a figure of merit for the experimental resolution of quantum features of a maser field. Therefore, a high resolution in the measurements of Rabi oscillations is crucial. This thesis describes the methods and improvements applied to enhance the resolution of Rabi oscillations by a factor of 8. The following upgrades and developments proved to be crucial in this work: 1) The base temperature of the cryogenic system was lowered to 0.3 K, i.e. one third of the original value. At the same time, the time during which the system remains at the base temperature was improved by almost of an order of magnitude (to more than 12 h). 2) For the promotion of the atoms to the Rydberg regime new three-step diode laser setup was constructed. The excitation efficiency compared to the old dye laser was increased by two orders. Using top-of-fringe stabilization with new spectroscopic methods, specially designed error detection and feedback schemes as well as state-of-the-art PID regulators the continuous locking of lasers is about 8 h (compared to about 20 min with the old dye laser system). 3) The flexibility of using the three step excitation allows to excite different maser states and for the first time to investigate pure maser transition. 4) Various improvements on the atomic oven and the channeltron detection unit led to the reliable and stable production and detection of the atomic beam. Observed distribution of the atomic beam statistics reaches to within 6% the Poisson limit which is expected in the absence of experimental imperfections. 5) New developed techniques in magnetic field compensation allow to perform such measurements with two orders of magnitude better accuracy compared to the previous experiments. To demonstrate the new capabilities of the apparatus and to apply its improved resolution of quantum fields we performed a previously impossible in-depth analysis of mean photon number and the atomic inversion produced by a micromaser for various detunings between the cavity- and atomic resonance frequency.