Relaxation- and decoherence-free subspaces in networks of weakly and strongly coupled resonators

Abstract

We consider a network of interacting resonators and analyze the physical ingredients that enable the emergence of relaxation-free and decoherence-free subspaces. We investigate two different situations: i) when the whole network interacts with a common reservoir and ii) when each resonator, strongly coupled to each other, interacts with its own reservoir. Our main result is that both subspaces are generated when all the resonators couple with the same group of reservoir modes, thus building up a correlation (among these modes), which has the potential to shield particular network states against relaxation and/or decoherence.The search for mechanisms to bypass decoherence, a subject of major concern for quantum information processing, has deepened our understanding of open quantum systems and led to ingenious schemes for coherence control, which go far beyond the quest for conditions that weaken the system-reservoir coupling [1,2]. The myriad contributions to this subject started, inspired by classical error-correcting codes, with quantum coding schemes for information stored in a quantum memory [3]. On the assumption that the decoherence process acts independently on each of the qubits stored in a memory, a particular qubit encoded in a block of ancillary qubits is able to withstand a substantial degree of interaction with the reservoir without degradation of its information. Another strategy, the so-called engineering reservoirs [4], compels the system of interest, whose state is to be protected against decoherence, to engage in additional interactions besides that with the reservoir. This program, based on the indirect control of system-reservoir dynamics, has been developed for trapped ions [5,6] and atomic two-level systems [7,8] as well. Finally, the process of collective decoherence, where a composite system interacts with a common reservoir, has also instigated several interesting results related to what has been called a decoherence-free subspace (DFS) [9,10,11]. It is noteworthy that while quantum error-correcting codes presuppose quantum systems that decohere independently, DFS -as it has been understood until the present study -is generated by distinct quantum systems coupled to a common reservoir.In this contribution we are concerned with collective dissipation and decoherence in a network of N coupled resonators. We analyze the physical ingredients ruling the emergence of a DFS and, in particular, a relaxationfree subspace (RFS) composed of states protected against both dissipation and decoherence, demonstrating that a DFS contains a RFS. We first analyze the situation, treated in the literature to date, where all the resonators are coupled to a common reservoir. However, as the scenario of a common reservoir is in practice rather unusual, we next analyze the situation where each resonator interacts with its own reservoir, which seems to be more appropriate for most physical systems. In the domain of cavity quantum electrodynamics, distinct reservoirs must be considered for distinguishable cavities,...

Storing quantum states in bosonic dissipative networks

“…Beyond the entanglement dynamics which is a crucial but recurrent ingredient of any network, the collective damping effects coming from two-atom systems [21] can be directly identified with those in a network of dissipative oscillators [16,18,19,20]. Such collective damping effect are certainly in the basis of the nonadditivity of decoherence rates observed in the network of dissipative oscillators [16,18,19,20] as well as in superconducting qubits [22].…”

“…A generalized analysis of decoherence for the case of a symmetric network of dissipative oscillators is presented in Ref. [20], where the physical ingredients that enable the emergence of relaxation-free and decoherence-free subspaces are exposed. On this regard, a detailed study of the optimum topologies leading to maximum decoherence times of superposition states prepared in particular oscillators of dissipative networks will be presented elsewhere [23].…”

“…From such development, a detailed analyzes of the emergence of relaxation-and decoherence-free subspaces in networks of weakly and strongly coupled resonators is presented in Ref. [20]. The main result in Ref.…”

“…The main result in Ref. [20] is that both subspaces are generated when all the resonators couple with the same group of reservoir modes, thus building up a correlation (among these modes), which has the potential to shield particular network states against relaxation and/or decoherence.…”

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“…The coupling results in an coherent hopping rate κ between cavities. We designateâ i andσ i as the field annihilation operator and atomic electron energy lowering operator for the i th JC cell, and the double JC cell Hamiltonian is [7,[9][10][11][12] H =Ĥ (12) for ν denoting the total number of quanta shared in the twocavity system.…”