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A photon counting and a squeezing measurement method by the exact absorption and dispersion spectrum of Λ-type Atoms

Ghasem Naeimi, Samira Alipour, Siamak Khademi

Published Aug 24, 2016• 1 citation
Publisher

Abstract

Recently, the master equations for the interaction of two-mode photons with a three-level Λ-type atom are exactly solved for the coherence terms. In this paper the exact absorption spectrum is applied for the presentation of a non-demolition photon counting method, for a few number of coupling photons, and its benefits are discussed. The exact scheme is also applied where the coupling photons are squeezed and the photon counting method is also developed for the measurement of the squeezing parameter of the coupling photons.

DOI
10.1186/s40064-016-3014-7

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Recently, the master equations for the interaction of two-mode photons with a three-level Λ-type atom are exactly solved for the coherence terms. In this paper the exact absorption spectrum is applied for the presentation of a non-demolition photon counting method, for a few number of coupling photons, and its benefits are discussed. The exact scheme is also applied where the coupling photons are squeezed and the photon counting method is also developed for the measurement of the squeezing parameter of the coupling photons.
The semi-classical model of atomfield interaction has been fully studied for some multilevel atoms, e.g.Vee, , Cascade  , Y, and inverted Y and so on.This issue is developed into the full-quantum electrodynamics formalism, where the probe and coupling electromagnetic fields are quantized.In this article, we investigate the full-quantum model of absorption and dispersion spectrum of trapped four-levels inverted Y type atoms, interacting with a probe beam of photons as well as two-mode trapped coupling photons.It is shown that the measurement of the maximum of absorption of the probe field and its detuning gives us simply the number of two-mode coupling photons, individually.An experimental setup for this non-demolition photon counting method is proposed and the numbers of coupling photons are obtained analytically.
The squeezing spectrum for a cavity field mode interacting with an ensemble of three-level ``\ensuremath{\Lambda}-configuration'' atoms by an effective two-photon transition is calculated. The advantage of the three-level \ensuremath{\Lambda} system as a squeezing medium, that is, optical nonlinearity without atomic saturation, has recently been pointed out by Reid, Walls, and Dalton. We predict perfect squeezing at the turning points for dispersive optical bistability and good squeezing for a range of other cases. Three-level ladder atoms interacting by an effective two-photon transition are also shown to give perfect squeezing in the dispersive limit.
Semi-quantum or full-quantum electromagnetically induced transparency has been fully studied for three-level atoms in a weak field approximation method, where probe field is very wea ker than the coupling field. The weak field approximation is no t valid in full-quantum model where the number of coupling photons is not so large. In the present article, the master equations for the interaction of two-mode photons with a three-level Λ -type atom are exactly solved and the exact dispersion and absorption spectra for the probe beam photons are also obtained analytically. The results of the exact scheme are compared with the corresponding results in the weak field approximation method in full-quantum and semi-classi cal models.
We consider a four-level atomic system in inverted-Y system and study the phenomenon of Electromagnetically Induced Transparency (EIT) in this system in interaction with three quantized fields (one probe field and two coupling fields) by full quantum model. The results indicate dependency of the interval between peaks and their altitude in absorption curve of probe field on number of coupling field photons’ that trapped inside the quantum cavity. In this paper a non-demolition photon counting method has been offered for two different kind of photons that belong to coupling fields that interact with an ensemble of four-level Inverted-Y type atoms and a quantize probe field by analytical calculation of density matrix equations.
We theoretically investigate the quantum statistical properties of a two-mode cavity light generated by a ∨ -type three-level atom interacting with nondegenerate subharmonic light and coupled to a two-mode squeezed vacuum reservoir. Using the master equation, we obtain steady-state expectation values for the atomic and cavity-mode operators. Based on these results, we analyze the global and local photon number variances, intensity fluctuation spectrum, joint photon number distribution, and photon count statistics. Our results reveal that squeezing parameter and subharmonic generation significantly enhance intensity fluctuations, as well as the mean and variance of photon counts, whereas atom-field coupling and cavity decay suppress them. The system exhibits super-Poissonian photon statistics, indicating that photon number fluctuations exceed the mean photon number. Furthermore, the photon count variance, which incorporates intracavity transmission and input noise, increases with detector efficiency. These results provide a comprehensive picture of photon statistics in atom-photon systems and guide the design of advanced quantum optical devices.
We study the interaction of a three-level atom with a single mode field through multiphoton transition in a cavity, taking explicitly into account the existence of forms of nonlinearities of both the field and the intensity-dependent atom-field coupling. The analytical forms of the absorption spectrum is calculated using the dressed states of the system. The effects of photon multiplicities, mean photon number, detuning, Kerr-like medium, and the intensity-dependent coupling functional on the absorption spectrum are analyzed.