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Physical Review A

Decoherence measurement of two coupled micromasers

Stefan Rinner, E. Werner, Thomas Matthias Becker, HERBERT WALTHER

Published Oct 9, 2006• 5 citations
Publisher

Abstract

We present a setup of two coupled micromaser cavities for studying decoherence. The system is prepared in a state where, initially, one photon is contained in one of the two cavities. The coupling of the two resonators allows the photon to tunnel into the other cavity with a certain probability. The system thus oscillates between the two states $\ensuremath{\mid}1{⟩}_{L}\ensuremath{\mid}0{⟩}_{R}$ and $\ensuremath{\mid}0{⟩}_{L}\ensuremath{\mid}1{⟩}_{R}$. It is shown how to map these states onto the states $\ensuremath{\mid}g⟩$ and $\ensuremath{\mid}e⟩$ of probe atoms used to investigate the status of the cavity system. It is an important result that the symmetry of our special setup allows decoherence to be monitored by measuring just the diagonal elements of the atomic density matrix. This property relies on the fact that only $\ensuremath{\mid}0⟩$ and $\ensuremath{\mid}1⟩$ states are relevant. To our knowledge, this is the first proposal that tries to exploit this particular property.

DOI
10.1103/physreva.74.041802

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We present a setup of two coupled micromaser cavities for studying decoherence. The system is prepared in a state where, initially, one photon is contained in one of the two cavities. The coupling of the two resonators allows the photon to tunnel into the other cavity with a certain probability. The system thus oscillates between the two states \ensuremath∣1⟩L\ensuremath∣0⟩R\ensuremath{\mid}1{⟩}_{L}\ensuremath{\mid}0{⟩}_{R}\ensuremath∣1⟩L​\ensuremath∣0⟩R​ and \ensuremath∣0⟩L\ensuremath∣1⟩R\ensuremath{\mid}0{⟩}_{L}\ensuremath{\mid}1{⟩}_{R}\ensuremath∣0⟩L​\ensuremath∣1⟩R​. It is shown how to map these states onto the states \ensuremath∣g⟩\ensuremath{\mid}g⟩\ensuremath∣g⟩ and \ensuremath∣e⟩\ensuremath{\mid}e⟩\ensuremath∣e⟩ of probe atoms used to investigate the status of the cavity system. It is an important result that the symmetry of our special setup allows decoherence to be monitored by measuring just the diagonal elements of the atomic density matrix. This property relies on the fact that only \ensuremath∣0⟩\ensuremath{\mid}0⟩\ensuremath∣0⟩ and \ensuremath∣1⟩\ensuremath{\mid}1⟩\ensuremath∣1⟩ states are relevant. To our knowledge, this is the first proposal that tries to exploit this particular property.
In a micromaser where a classical field strongly drives the atoms while they cross the cavity, remarkable atom–atom correlations show up at steady state, which vanish much faster than dissipative decay. Hence we consider atom pair correlation measurements in which the detection of the first probe atom prepares a mesoscopic superposition state of the cavity field, that entangles with a second probe atom. The conditional probabilities for the latter atomic detection provide a description of the decoherence of the superposition state, occurring in an open system in the presence of pumping, driving, dissipative, and thermal effects. The decoherence rate scales as the squared interaction time, that sets the separation in phase space between the superposition components, whereas the quantum coherence is unaffected by the atomic pumping. Hence we further investigate the system when the cavity is not pumped. Starting the correlation measurements from a thermal state, we can describe the effect of temperature on decoherence. Starting from a vacuum state, the superposition states are maximally separated Schrodinger cat states, whose decoherence can thus be monitored.
We discuss a possible realization of a quantum register with controllable decoherence in terms of /0> and /1> photon number states of a micromaser field. It is shown how to create in the Jaynes-Cummings model a superposition state of /0> and /1> photon number states inside a closed micromaser cavity. The loss of phase coherence between these two states can subsequently be measured by a second probe atom monitoring the decoherence of the field. A technique is proposed for forming the superposition of number states /0> and /1> using the time structure of the Rabi oscillation. The proposed method avoids problems with stray fields at the cavity holes, which disturb the coherence of the atomic superposition, and offers a way to study how the coupling strength to the environment influences the decoherence rate, displaying the robustness of physical qubits and the fidelity of quantum computations.
Detailed theoretical and experimental study of the atom–field interaction starting from first principles was made possible by the realization of the single-atom micromaser. 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 superconducting cavity. This system's ability to coherently transfer quantum states between atoms and photons made it relevant in the context of quantum computation as well. Although considerable work, both theoretical and experimental, has been devoted to this system, with a few exceptions, most cases involved only non-coherent pumping. As a result, the density matrix describing the cavity field remained diagonal, preventing the appearance of coherences. Here, our goal is to provide a summary of the progress we made toward a comprehensive understanding of the features of the coherently pumped micromaser with special respect to coherences, which are central to quantum information processing.
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.
We show that two-atom correlation measurements of the type involved in a recent experimental study of the evolution of a mesoscopic superposition state prepared in a definite mode of a high-QQQ cavity can be used to determine the eigenvalues of the reduced density matrix of the field, provided the assumed dynamical conditions are actually fulfilled to experimental accuracy. These conditions involve (i) a purely dispersive coupling of the field to the Rydberg atoms used to manipulate and to monitor the cavity field, and (ii) the effective absence of correlations in the ground state of the system consisting of the cavity coupled to the ``reservoir'' which accounts for the decoherence and damping processes. A microscopic calculation at zero temperature is performed and compared to master equation results.