Improving coherence with nested environments

Abstract

We have in mind a register of qubits for an quantum information system, and consider its decoherence in an idealized but typical situation. Spontaneous decay and other couplings to the far environment considered as the world outside the quantum apparatus will be neglected, while couplings to quantum states within the apparatus, i.e. to a near environment are assumed to dominate. Thus the central system couples to the near environment which in turn couples to a far environment. Considering that the dynamics in the near environment is not sufficiently well known or controllable, we shall use random matrix methods to obtain analytic results. We consider a simplified situation where the central system suffers weak dephasing from the near environment, which in turn is coupled randomly to the far environment. We find the anti-intuitive result that increasing the coupling between near and far environment actually protects the central qubit. In many quantum optics experiments and quantum information devices we find the following situation: The central system, well protected from simple decoherence processes such as spontaneous emission or direct coupling to a structureless heat bath, still suffers some decoherence from the coupling to the quantum part of the apparatus. We will call the former the far environment and the latter the near environment. In such a tripartite system without direct coupling between central system and far environment, we find that increasing the coupling of the near to the far environment can protect the central system against decoherence. In the setting of the Haroche experiment [1, 2] the late M. C. Nemes discussed this somewhat anti-intuitive fact with one of the authors [3] twelve years ago. More recently, additional numerical evidence has appeared [4], some of which were master thesis related to the present work [5][6][7]. Finally, it was shown in Ref.[8] that a protected subspace can appear in a strong coupling limit.We now wish to construct a model that allows some analytical treatment and simultaneously has some claim to universality. Indeed the intermediate environment in a quantum information system typically consists of quantum states that are not used but are unavoidably present. While ordered and systematic couplings can be minimized with good technology, it is plausible that the uncontrolled remanent will have a random structure. Considering its minimum information character [9], we use random matrix theory (RMT) of decoherence [10][11][12]. There are several examples, which involve chaotic or irregular dynamics explicitly: e.g. the coupling of two-level atoms to quantum systems with classical chaotic analog [13,14], and the experimental realization of quantum chaos in a chain of three level atoms in [15]. The recent advances in the design and control of chains of individual ions [16], may lead to similar experimental systems. We simplify the picture by limiting the coupling between central system and near environment to dephasing [17,18], and assume the coupling between near and f...

Protecting coherence by environmental decoherence: a solvable paradigmatic model

“…The unitary Hamiltonian which causes an oscillation of the excitation between the spin and the oscillator is effective. For stronger coupling this dynamics loses importance until we reach a total freeze of dynamics including purity; this is in agreement with the findings of [8]. There the protection of coherence by decoherence of the environment was shown in a weak coupling regime by linear response considerations, which also preclude a quantum Zeno effect.…”

“…With the dephasing Lindblad operator we have a very simple example, where we can see the entire development of decoherence as a function of time for different parameters. The scaling behavior is readily established and we see, that the same equation describes the improvement of decoherence from the perturbative all the way to the strong coupling regime, as could be hoped from the rather general analytic results implicit in [7][8][9]. Yet in the perturbative regime for κ it seemed that for chaotic environments in the Fermi golden rule regime, i.e.…”

“…The great benefit in this approach is that one does not require to control the system dynamically. Numerical results for spin systems [10] and random matrix environments [8] seem to support such improvement throughout the range of coupling strength. In all cases there seem to exist options to improve the persistence of coherence of the central system considerably if it is already quite good to start with.…”

“…Recent studies have considered the coherence loss of a 'near' environment to stabilize the coherence of a central quantum system. This reaches from the limit of very fast decoherence of the near environment [7][8][9][10][11], which may actually lead in some limit to a protected subspace for the central system, all the way to perturbative treatments where all couplings are small [8,9]. The great benefit in this approach is that one does not require to control the system dynamically.…”

“…Next, we will address the case of photon losses in the cavity in which the annihilation operator of the oscillator is considered as Lindblad operator. Finally, we shall discuss to what extent our considerations may shed light into known numerical and random matrix results [8][9][10], and discuss in what ways the basic result can be used to help control coherence.…”