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Journal of Modern Optics

Stepwise phase modulation of atoms coupled to a quasicontinuum of states in a cavity

Ilkka Juhani Tittonen, Stig Stenholm, Igor Jex

Published Jan 1, 1998• 2 citations
Publisher

Abstract

We study the interaction of a small number of resonant two-level atoms in a cavity coupled to a quasi-continuum of cavity modes. During the interaction we induce externally a phase step to one of the atoms. As a result an enhancement in the photon emission to the field is observed. The phase step is obtained by a pulse which causes the atom to be off-resonance for a short time interval. The effect is strongest in cases where the number of atoms is small. The enhancement is not restricted to a small parameter range but should be observable in many systems even though the φ phase shift gives the best enhancement.

DOI
10.1080/09500349808231666

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We study the interaction of a small number of resonant two-level atoms in a cavity coupled to a quasi-continuum of cavity modes. During the interaction we induce externally a phase step to one of the atoms. As a result an enhancement in the photon emission to the field is observed. The phase step is obtained by a pulse which causes the atom to be off-resonance for a short time interval. The effect is strongest in cases where the number of atoms is small. The enhancement is not restricted to a small parameter range but should be observable in many systems even though the φ phase shift gives the best enhancement.
We study the dynamics of a system composed of two coupled cavities, each interacting with a single Rydberg atom. The interplay between Rydberg-Rydberg interaction and photon hopping enables the transition of the atoms from the collective ground state to the double Rydberg excitation state by individually interacting with the optical normal modes and suppressing the upconversion process between them. The atomic transition is accompanied by the two-photon absorption and emission of the normal modes. Since the energy level structure of the atom-cavity system is photon number dependent there is only a pair of states being in the two-photon resonance. Therefore, the system can act as a quantum nonlinear absorption filter through the nonclassical quantum process, converting coherent light field into a nonclassical state. Meanwhile, the vacuum field in the cavity inspires the Rydberg atoms to simultaneously emit two photons into the normal mode, resulting in obvious emission enhancement of the mode.
The emission spectrum of a pair of effective two-level atoms interacting with two modes of the radiation field with different coupling constants through a multiphoton Raman process is studied. A general expression for the emission spectrum with two modes of the field being in arbitrary states is presented. Our results show that when two modes of the field are in arbitrary number states, the spectrum is always symmetric about the resonant frequency , although the Hamiltonian of the system is asymmetric which is induced by the two different atom-field coupling constants. This property is analysed with an analytic method.
The present study described about the interaction of a two level atom and squeezed field with time varying frequency. By applying a sinusoidal variation\nin the frequency of the field, the randomness in population inversion is reduced and the collapses and periodic revivals are regained. Quantum optics is an emerging field in physics which mainly deals with the interaction of atoms with quantised electromagnetic fields. Jaynes-Cummings Model (JCM) is a key model among them, which describes the interaction between a two level atom and a single mode radiation field. Here the study begins with a brief history of light, atom and their interactions. Also discussed the interaction between atoms and electromagnetic fields. The study suggest a method to manipulate the population inversion due to interaction and control the randomness in it, by applying a time dependence on the frequency of the interacting squeezed field.The change in behaviour of the population inversion due to the presence of a phase factor in the applied frequency variation is explained here.This study also describes the interaction between two level atom and electromagnetic field in nonlinear Kerr medium. It deals with atomic and field state evolution in a coupled cavity system. \nOur results suggest a new method to control and manipulate the population of states in two level atom radiation interaction,which is very essential for quantum information processing.We have also studied the variation of atomic population inversion with time, when a two level atom interacts with light field, where\nthe light field has a sinusoidal frequency variation with a constant phase. In both coherent field and squeezed field cases, the population inversion variation is completely different from the phase zero frequency modulation case. It is observed that in the presence of a non zero phase φ, the population inversion oscillates sinusoidally.Also the collapses and revivals gradually disappears when φ increases\nfrom 0 to π/2. When φ = π/2 the evolution of population inversion is identical to the case when a two level atom interacts with a Fock state. Thus, by applying a phase shifted frequency modulation one can induce sinusoidal oscillations of atomic inversion in linear medium, those normally observed in Kerr medium. \nWe noticed that the entanglement between the atom and field can be controlled by\nvarying the period of the field frequency fluctuations. The system has been solved numerically and the behaviour of it for different initial conditions and different susceptibility values are analysed. It is observed that, for weak cavity coupling the effect of susceptibility is minimal. In cases of strong cavity coupling, susceptibility factor modifies the nature in which the probability oscillates with time. Effect\nof susceptibility on probability of states is closely related to the initial state of the system.
Traditionally, strong-field physics explores phenomena in laser-driven matter (atoms, molecules, and solids) that cannot be understood by treating the laser field as a small perturbation. Therefore, the presence of an extremely strong external field is usually a prerequisite for observing strong-field phenomena. However, even in the complete absence of an external electromagnetic field, strong-field phenomena can arise when matter strongly couples with the zero-point field of the quantum vacuum state, i.e., fluctuating electromagnetic waves whose expectation value is zero. This can occur in free space where the matter strongly interacts with a continuum of photon modes, but some of the most striking examples of strong-field physics without an external field occur in a cavity setting, in which an ensemble of two-level atoms resonantly interacts with a single photonic mode of vacuum fields, producing vacuum Rabi splitting. In particular, the nature of the matter-vacuum-field coupled system fundamentally changes when the coupling rate (equal to one half of the vacuum Rabi splitting) becomes comparable to, or larger than, the resonance frequency. In this so-called ultrastrong coupling regime, a non-negligible number of photons exist in the ground state of the coupled system. Furthermore, the coupling rate can be cooperatively enhanced (via so-called Dicke cooperativity) when the matter is comprised of a large number of identical two-level particles, and a quantum phase transition is predicted to occur as the coupling rate reaches a critical value. Low-energy electronic or magnetic transitions in many-body condensed matter systems with large dipole moments are ideally suited for searching for these predicted phenomena. Here, we discuss two condensed matter systems that have shown cooperative ultrastrong interactions in the terahertz frequency range: a Landau-quantized two-dimensional electron gas interacting with high-quality-factor cavity photons, and an Er3+ spin ensemble interacting with Fe3+ magnons in ErFeO3.