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Fortschritte der Physik

Multiatomic Entanglement in a Decoherence Free Subspace

Péter Földi, M. G. Benedict, Attila Czirják

Published Oct 1, 2001• 0 citations
Publisher

Abstract

Subradiant states — as a special kind of entangled states of severel two-level atoms — have recently gained wide attention because these states are exceptional in the sense that they dissipate energy much slower then other collective states. This property implies also that their decoherence is slow, and henceforth they are promising candidates for registers of a quantum computer. Here we propose a scheme which can be used to prepare subradiant states in a cavity. We present perturbative and also exact results showing that after a certain time the evolution of a multiatomic system in a detuned cavity leads to an appropriate entangled state. At this time instant it is sufficient to apply subsequent laser pulses on a control atom in order prepare a state in the subradiant, i.e., a decoherence free subspace.

DOI
10.1002/1521-3978(200110)49:10/11<961::aid-prop961>3.0.co;2-n

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Subradiant states — as a special kind of entangled states of severel two-level atoms — have recently gained wide attention because these states are exceptional in the sense that they dissipate energy much slower then other collective states. This property implies also that their decoherence is slow, and henceforth they are promising candidates for registers of a quantum computer. Here we propose a scheme which can be used to prepare subradiant states in a cavity. We present perturbative and also exact results showing that after a certain time the evolution of a multiatomic system in a detuned cavity leads to an appropriate entangled state. At this time instant it is sufficient to apply subsequent laser pulses on a control atom in order prepare a state in the subradiant, i.e., a decoherence free subspace.
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.
The effect of decoherence in a quantum system can be viewed as a consequence of the interaction with the environment. As has been pointed out first 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 more slowly. We have recently proposed a scheme which is intended to create such states in a detuned cavity. We shall examine here the conditions under which our scheme can be used and compare them with the experimental possibilities. The analysis shows that our proposal can be implemented with present-day techniques achieved in atom—cavity interaction experiments.
We present analytical results on entanglement and decoherence in a system of N strongly driven two-level atoms resonantly coupled to a dissipative cavity mode. In the specific cases of N = 3 and 4 qubits we show the existence of decoherence-free subspaces for the whole system and/or the atomic subsystem and we discuss examples where a multipartite qubit entanglement remains preserved. Also we illustrate the conditional preparation of cat-like states of the cavity field and the generation of atomic correlations.
We propose schemes to design and control a time-dependent decoherence-free subspace (DFS) in a dissipative atom-cavity system. These schemes use atoms with three internal energy levels, which allows for the DFS to be multidimensional---a condition important for quantum sensing, simulation, and computation. We consider the use of tunable external driving lasers to transfer the system from a coherent spin state to a highly degenerate DFS. We find that the typical state in the DFS is highly entangled. Throughout evolution the state is kept in an instantaneous DFS, thereby allowing for pure states to be prepared. We develop adiabatic shortcuts to carry out this evolution with higher purity and fidelity than standard adiabatic and dissipative methods.
A scalable multatom entangled system, capable of high-performance quantum computations, can be realized by resonant dipole-dipole interacting dopants in a solid state host. In one realization, the qubits are represented by ground and subradiant states of effective dimers formed by pairs of closely spaced two-level systems (TLS). Such qubits are highly robust against radiative decay. The two-qubit entanglement in this scheme relies on coherent excitation exchange between the dimers by external laser fields. This scheme is challenging because of the nanosize control and addressability it requires. Another realization involves dipole-dipole interacting TLS whose resonance frequency lies in a photonic band gap of a dielectric photonic crystal. A sequence of abrupt changes of the resonance frequency can produce controlled entanglement (logic gates) with improved protection from radiation decay and decoherence.