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Alteration of decoherence-free states caused by dipole-dipole interactions

François Damanet, John Martin

Published Jun 23, 2014• 0 citations
OpenAlex

Abstract

Decoherence, known as the consequence of the coupling of any quantum system to its environment, causes information loss in the system and represents a major problem in the physical realization of quantum computers [1]. Decoherence-Free States (DFS) are considered as a possible solution to this problem. A set of trapped cold atoms placed in a DFS state will be immune against decoherence due to spontaneous emission. However, because of dipole-dipole interactions between atoms, induced dephasing effects are likely to destroy the coherence and drive the system out of its DFS [1, 2]. In this work, we study numerically the dynamics of a set of two-level atoms initially in a DFS with respect to dissipative processes by solving the master equation including both dissipative dynamics and dipole dipole interactions. We fo- cus our attention on the infuence of dipolar coupling on the radiated energy rate and coherence of the system as in [3]. In particular, by averaging over many realizations of close randomly distributed atomic positions, we show the formation of a superradiant-like pulse and we study its properties as a function of the dipolar coupling strength. [1] D. A. Lidar & K. B. Whaley, Lectures Notes in Phys., Vol. 622, p83-120, Springer (2003). [2] M. Gross & S. Haroche, Physics reports 93, 301-396 (1982). [3] W. Feng, Y. Li & S-Y. Zhu, Phys. Rev. A 88, 033856 (2013).

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Decoherence, known as the consequence of the coupling of any quantum system to its environment, causes information loss in the system and represents a major problem in the physical realization of quantum computers [1]. Decoherence-Free States (DFS) are considered as a possible solution to this problem. A set of trapped cold atoms placed in a DFS state will be immune against decoherence due to spontaneous emission. However, because of dipole-dipole interactions between atoms, induced dephasing effects are likely to destroy the coherence and drive the system out of its DFS [1, 2]. In this work, we study numerically the dynamics of a set of two-level atoms initially in a DFS with respect to dissipative processes by solving the master equation including both dissipative dynamics and dipole dipole interactions. We fo- cus our attention on the infuence of dipolar coupling on the radiated energy rate and coherence of the system as in [3]. In particular, by averaging over many realizations of close randomly distributed atomic positions, we show the formation of a superradiant-like pulse and we study its properties as a function of the dipolar coupling strength. [1] D. A. Lidar & K. B. Whaley, Lectures Notes in Phys., Vol. 622, p83-120, Springer (2003). [2] M. Gross & S. Haroche, Physics reports 93, 301-396 (1982). [3] W. Feng, Y. Li & S-Y. Zhu, Phys. Rev. A 88, 033856 (2013).
The time evolution of short linear chains consisting of dipole coupled two-level systems (atoms) is investigated under the influence of oscillator modes, which represent the environment. The dynamics of the system is calculated using the super-radiant master equation. The focus is on phenomena related to the environment induced decoherence and entanglement degradation. For large atomic distances the initially present pair entanglement is destroyed independently from the spatial position of the two atoms, while when the distance between the atoms becomes comparable to the resonant wavelength the rate of entanglement degradation corresponds to the strength of the pair interaction. Below one resonant wavelength of atomic separation, formation of pair entanglement is also possible in the initial stage of the time evolution. In this case it is found that pair entanglement is formed and destroyed periodically, and the strengths of the consecutive ‘entanglement revivals’ are damped depending on the initial state. The subradiant states, for which decoherence is slow, also preserve pair entanglements for an exceptionally long time.
The cause of decoherence in a quantum system can be traced back to the interaction with the environment. As it has been pointed out by Dicke, in a system of N two-level atoms, where each of the atoms is individually dipole coupled to the environment, there are collective, subradiant states, that have no dipole coupling to photon modes, and therefore, they are expected to decay slower. This property also implies that these type of states decohere slower. We propose a scheme which will create such states. First, the two-level atoms are placed in a strongly detuned cavity and one of the atoms, called the control atom is excited. The time evolution of the coupled atom-cavity system leads to an appropriately entangled state of the atoms. By the aid of a suitable single-atom phase transformation, it is possible to drive the atomic state into the subradiant, i.e., decoherence-free subspace. Up to a certain average number of photons, the result is independent of the state of the cavity. The analysis of the conditions shows that this scheme is feasible with present day techniques achieved in atom-cavity interaction experiments.
Enhanced and inhibited spontaneous emission of two close atoms in an overdamped cavity is studied taking into account the dipole-dipole interaction between them. The system is described in the minimal-coupling scheme and the advantages of this choice for our problem are discussed. The dynamics is investigated using both quantum Langevin equations and Master equation techniques. This last approach allows one to describe the behavior of the atoms plus field system as a one-step process. The case in which both atoms are initially in their excited state and the mode is in its vacuum state is discussed in some detail. It is shown that, different from what occurs to two close atoms in free space, in an overdamped cavity dipolar interaction may modify the decay rate. In particular, we find that the two transitions the atomic system performs to reach its equilibrium configuration can have different rates, and that for a suitable choice of the detuning between the cavity mode and the unperturbed atomic frequency, one of the transitions occurs at an enhanced rate while the second is inhibited.
Electron dynamics in dipole-dipole (DD) coupled Rydberg atoms show some unique properties that do not exist in individual atoms.The goal of the research in this dissertation is to reveal and control the electron dynamics influenced by DD interaction in cold Rydberg gases.We have studied the decay of Rydberg excitations in a cold Rb gas and find no evidence for superradiance.The decay rates and population redistribution we observe are consistent with a model that considers only spontaneous emission from, and blackbody redistribution within, isolated atoms.Suppression of superradiant emission is likely due to variations in transition energies across the cold Rydberg atom sample.For initial s states, these variations are dominated by inhomogeneities in DD exchange interactions within the random ensemble.Such inhomogeneities will necessarily be present in any measurement involving a large number of atoms where the separation between atoms is not well defined.For initial p states, the suppression is likely due to a combination of DD exchange and electric field inhomogeneities.We have also explored the evolution of Rydberg wavepackets in the presence of strong dipole-dipole interactions in a frozen gas.The distribution of atom separations results in an inhomogeneity in the strength of the exchange coupling between neighboring atoms, causing a dephasing of the macroscopic coherence.We have also explored the mechanism of wavepacket coherence transfer from one Rydberg atom to a neighboring Rydberg atom via DD interactions utilizing the resonant DD coupling transition 25s33s↔24p34p.The phase-shift of the observed interference modulations in the 34p signal, relative to that in 25s, is a signature of wavepacket coherence transfer between atoms driven by electron correlations resulting from the controlled DD coupling between them.I would like to thank my advisor Professor Bob Jones for his guidance and help, not only in the detailed research performance but also in scientific ethics and methodology.He taught me how to operate most of the instruments as well as helped me fix failing apparatus.His rigorous, yet optimistic, working attitude always inspires me in my research.I don't remember how many times I have felt frustrated after getting nothing from a several days' experiment.At those times, I was always motivated and energetic from his guidance, constructive criticism and sincere encouragement, after even a short talk with him.The accomplishment of this dissertation involved a lot of his help, ranging from grammar checking, to language polishing, to error correction.I really feel grateful and fortunate to have worked with him for more than 5 years.Thanks also goes to my colleagues who have helped me in the research.Brian Richards worked with me a lot to fix failing instruments.He also programmed the data collection software.Sha Li taught me how to build setups to generate the THz radiation and build dye lasers.Kisra Nayomal Egodapitiya helped me adjust lasers and amplifiers many times.I also got invaluable inspiration from daily talks with them.
Quantum interference and coherence effects in the interaction of atoms with the quantized electromagnetic field are investigated theoretically. A general master equation for the description of atom-field interactions is introduced. The interplay of the concepts of complementarity and interference in the time-energy domain are studied on the basis of the fluorescence light emitted by a single laser-driven atom, where the coherence of spontaneous processes gives rise to quantum interference in the spectrum of resonance fluorescence. The vacuum-induced dipole-dipole interaction in pairs of multi-level atoms is analyzed. It is shown that the interaction between orthogonal transition dipole moments of different atoms does not only influence the system dynamics crucially, but implies that the few-level approximation in general cannot be applied to near-degenerate Zeeman sublevels of the atomic level scheme. Potential applications of dipole-dipole interacting multi-level atoms for the implementation of decoherence-free subspaces and the generation of entanglement between atomic states are examined. The generation of an entangled state of the radiation field with a macroscopic number of photons is discussed on the basis of a single-atom laser.
Summary form only given. Controlled coherent interactions between pairs of neutral atoms can be designed in tight micro-traps such as optical lattices which allow the creation of highly entangled multiparticle states. Such systems benefit from suppressed decoherence because neutrals couple weakly to the environment and the interactions are strictly pairwise. The main source of decoherence is spontaneous emission which can be made negligible if the two atom interactions are performed fast compared to the scattering rate.We have shown the possibility of using induced electric dipole-dipole interactions between pairs of atoms to perform quantum logic gates with high fidelity.