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Journal of Physics Condensed Matter

Vibrons in finite size molecular lattices: a route for high-fidelity quantum state transfer at room temperature

Vincent Pouthier

Published Oct 9, 2012• 13 citations
Publisher

Abstract

A communication protocol is proposed in which vibron-mediated quantum state transfer takes place in a molecular lattice. We consider two distant molecular groups grafted on each side of the lattice. These groups form two quantum computers where vibrational qubits are implemented and received. The lattice defines the communication channel along which a vibron delocalizes and interacts with a phonon bath. Using quasi-degenerate perturbation theory, vibron-phonon entanglement is taken into account through the effective Hamiltonian concept. A vibron is thus dressed by a virtual phonon cloud whereas a phonon is clothed by virtual vibronic transitions. It is shown that three quasi-degenerate dressed states define the relevant paths followed by a vibron to tunnel between the computers. When the coupling between the computers and the lattice is judiciously chosen, constructive interference takes place between these paths. Phonon-induced decoherence is minimized and a high-fidelity quantum state transfer occurs over a broad temperature range.

DOI
10.1088/0953-8984/24/44/445401

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A communication protocol is proposed in which vibron-mediated quantum state transfer takes place in a molecular lattice. We consider two distant molecular groups grafted on each side of the lattice. These groups form two quantum computers where vibrational qubits are implemented and received. The lattice defines the communication channel along which a vibron delocalizes and interacts with a phonon bath. Using quasi-degenerate perturbation theory, vibron-phonon entanglement is taken into account through the effective Hamiltonian concept. A vibron is thus dressed by a virtual phonon cloud whereas a phonon is clothed by virtual vibronic transitions. It is shown that three quasi-degenerate dressed states define the relevant paths followed by a vibron to tunnel between the computers. When the coupling between the computers and the lattice is judiciously chosen, constructive interference takes place between these paths. Phonon-induced decoherence is minimized and a high-fidelity quantum state transfer occurs over a broad temperature range.
A communication protocol is proposed in which quantum state transfer is mediated by a vibrational exciton. We consider two distant molecular groups grafted on the sides of a lattice. These groups behave as two quantum computers where the information in encoded and received. The lattice plays the role of a communication channel along which the exciton propagates and interacts with a phonon bath. Special attention is paid for describing the system involving an exciton dressed by a single phonon mode. The Hamiltonian is thus solved exactly so that the relevance of the perturbation theory is checked. Within the nonadiabatic weak-coupling limit, it is shown that the system supports three quasi-degenerate states that define the relevant paths followed by the exciton to tunnel between the computers. When the model parameters are judiciously chosen, constructive interferences take place between these paths. Phonon-induced decoherence is minimized and a high-fidelity quantum state transfer occurs over a broad temperature range.
A communication protocol is proposed in which quantum state transfer is mediated by a vibrational exciton. We consider two distant molecular groups grafted on the sides of a one-dimensional lattice. These groups behave as two quantum computers where the information in encoded and received. The lattice plays the role of a communication channel along which the exciton propagates and interacts with a phonon bath. Special attention is paid to describing the system involving an exciton dressed by a single phonon mode. The Hamiltonian is thus solved exactly so that the relevance of the perturbation theory is checked. Within the nonadiabatic weak-coupling limit, it is shown that the system supports three quasidegenerate states that define the relevant paths followed by the exciton to tunnel between the computers. When the model parameters are judiciously chosen, constructive interferences take place between these paths. Phonon-induced decoherence is minimized and a high-fidelity quantum state transfer occurs over a broad temperature range.
The exciton-phonon system in a confined environment is revisited within standard perturbation theory. Special attention is paid to describing the time evolution of the excitonic coherences at finite temperature. To proceed, the system involving an exciton dressed by a single phonon mode is considered. Owing to its simplicity, it is solved exactly so that the relevance of the perturbation theory is checked. Within the nonadiabatic weak-coupling limit, it is shown that several time scales govern the coherence dynamics. In the short-time limit, the coherences behave as if the exciton was insensitive to the phonon bath. Then, quantum decoherence takes place. Finally the coherences recur almost periodically at specific revival times. Coherence decay and revival strongly depend on the nature of the excitonic states. In particular, for odd lattice sizes, the coherence of the state exactly located at the band center survives over a very long-time scale. Therefore, confinement-induced decoherence softening favors high-fidelity quantum-state transfer and allows to encode the information on a quantum bit almost insensitive to quantum decoherence.
The lifetime of two-vibron bound states in the overtone region of a one-dimensional anharmonic molecular lattice is investigated. The anharmonicity, introduced within an attractive Hubbard Hamiltonian for bosons, is responsible for the formation of bound states which belong to a finite linewidth band located below the continuum of two-vibron free states. The decay of these bound states into either bound or free states is described by considering the coupling between the vibrons and a thermal bath formed by a set of low-frequency acoustic phonons. The relaxation rate is expressed in terms of the spectral distribution of the vibron/phonon coupling and of the two-vibron Green operator which is calculated exactly by using the number states method. The behavior of the two-vibron bound states relaxation rate is analyzed with a special emphasis on the influence of the anharmonicity. It is shown that the rate exhibits two distinct regimes depending on the thermal bath dimension. When the bath dimension is equal to unity, the rate increases with the anharmonicity and the decay of the two-vibron bound states into the other bound states appears as the main contribution of the rate. By contrast, when the bath dimension is equal to 2 and 3, the rate decreases as the anharmonicity increases, indicating that the two-vibron bound states decay into the two-vibron free states continuum.
We study collective excitations of rotational and spin states of an ensemble of polar molecules, which are prepared in a dipolar crystalline phase, as a candidate for a high-fidelity quantum memory. While dipolar crystals are formed in the high-density limit of cold clouds of polar molecules under one- and two-dimensional trapping conditions, the crystalline structure protects the molecular qubits from detrimental effects of short-range collisions. We calculate the lifetime of the quantum memory by identifying the dominant decoherence mechanisms, and estimate their effects on gate operations, when a molecular ensemble qubit is transferred to a superconducting strip line cavity (circuit QED). In the case of rotational excitations coupled by dipole-dipole interactions we identify phonons as the main limitation of the lifetime of qubits. We study specific setups and conditions, where the coupling to the phonon modes is minimized. Detailed results are presented for a one-dimensional dipolar chain.
An attempt is made to measure the vibron-phonon coupling strength in a finite size lattice of H-bonded peptide units. Within a finite temperature density matrix approach, we compare separately the influence of both the vibron-phonon coupling and the dipole-dipole interaction on the coherence between the ground state and a local one-vibron state. Due to the confinement, it is shown that the vibron-phonon coupling yields a series of dephasing-rephasing mechanisms that prevents the coherence to decay. Similarly, the dipole-dipole interaction gives rise to quantum recurrences for specific revival times. Nevertheless, intense recurrences are rather rare events so that the coherence behaves as a random variable whose most probable value vanishes. By comparing the degree of the coherence for each interaction, a critical coupling chi*(L) is defined to discriminate between the weak and the strong coupling limits. Its size dependence indicates that the smaller the lattice size is, the weaker the vibron-phonon coupling relative to the dipole-dipole interaction is.