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RSUH/RGGU Bulletin Series Information Science Information Security Mathematics

DECOHERENCE-FREE STORAGE INFORMATION SPACE

Maksim S. Zemlyak, Nadezhda B. Victorova

Published Jan 1, 2020• 0 citations
Publisher

Abstract

Quantum systems are of great interest in current realities. Quantum computers are not an alternative to the classic. Rather, they can be attributed to the class of devices specializing in a separate group of tasks. However, a key issue in the design of quantum computers is the issue of decoherence time. To combat that phenomenon, various methods of isolating a quantum system are being developed, including the use of extremely low temperatures and high vacuum. In addition, one of the ways to combat decoherence is to use dark states, due to the fact that a system of atoms in this state is not able to interact with light – absorb or emit photons. In this paper, various systems of three-level atoms are considered. Schemes of two types of atoms are represented graphically – λ-atoms, v-atoms. The concept of a dark quantum state and the concept of a family of a quantum state are introduced. An algorithm for finding the dimension and basis of the subspace of dark states is presented. According to the algorithm, the dimensions and bases of the subspaces of dark states in these systems are calculated.

DOI
10.28995/2686-679x-2020-2-72-84

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Quantum systems are of great interest in current realities. Quantum computers are not an alternative to the classic. Rather, they can be attributed to the class of devices specializing in a separate group of tasks. However, a key issue in the design of quantum computers is the issue of decoherence time. To combat that phenomenon, various methods of isolating a quantum system are being developed, including the use of extremely low temperatures and high vacuum. In addition, one of the ways to combat decoherence is to use dark states, due to the fact that a system of atoms in this state is not able to interact with light – absorb or emit photons. In this paper, various systems of three-level atoms are considered. Schemes of two types of atoms are represented graphically – λ-atoms, v-atoms. The concept of a dark quantum state and the concept of a family of a quantum state are introduced. An algorithm for finding the dimension and basis of the subspace of dark states is presented. According to the algorithm, the dimensions and bases of the subspaces of dark states in these systems are calculated.
Abstract Dark states of atomic ensembles do not interact with light (can neither emit nor absorb a single photon due to destructive interference). Being free of decoherence, they can be widely used in quantum computing (particularly as a mechanism for creating quantum memory). To date, the structure of dark states of two-level atoms has been sufficiently well studied; meanwhile, this problem remains open for three-level atomic ensembles. For ensembles of two-level atoms (in a chosen range), it was established that the dimension of the dark subspace is equal to the Catalan numbers. It is difficult to generalize this statement to the case of three-level, and even more so, multi-level atomic ensembles and has not been done so far. This paper proposes a supercomputer algorithm for numerical confirmation of a similar statement for ensembles of a limited number (not exceeding several tens) of three-level atoms.
The dark states of a group of two-level atoms in the Tavis-Cummings resonator with zero detuning are considered. In these states, atoms can not emit photons, despite having non-zero energy. They are stable and can serve as a controlled energy reservoir from which photons can be extracted by differentiated effects on atoms, for example, their spatial separation. Dark states are the simplest example of a subspace free of decoherence in the form of a photon flight, and therefore they are of interest to quantum computing. It is proved that a) the dimension of the subspace of dark states of atoms is the Catalan numbers, b) in the RWA approximation, any dark state is a linear combination of tensor products of singlet-type states and the ground states of individual atoms. For the exact model, in the case of the same force of interaction of atoms with the field, the same decomposition is true, and only singlets participate in the products and the dark states can neither emit a photon nor absorb it. The proof is based on the method of quantization of the amplitude of states of atomic ensembles, in which the roles of individual atoms are interchangeable. In such an ensemble there is a possibility of micro-causality: the trajectory of each quantum of amplitude can be uniquely assigned. Рассматриваются темные состояния группы двух-уровневых атомов в резонаторе модели Тависа-Каммингса с нулевой расстройкой. В этих состояниях атомы не могут испустить фотона, хотя обладают ненулевой энергией. Они устойчивы и могут служить управляемым энергетическим резервуаром, из которого можно извлечь фотоны путем дифференцированного воздействия на атомы, например, их пространственного разделения. Темные состояния - простейший пример подпространства, свободного от декогерентности в виде улета фотонов, и потому представляют интерес для квантовых вычислений. Доказано, что а) размерность подпространства темных состояний атомов есть числа Каталана, б) В RWA приближении любое темное состояние есть линейная комбинация тензорных произведений состояний синглетного типа и основных состояний отдельных атомов. Для точной модели в случае одинаковой силы взаимодействия атомов с полем справедливо то же разложение, причем в произведениях участвуют только синглеты и темные состояния не могут ни испустить фотона, ни поглотить его. Доказательство основано на методе квантования амплитуды состояний атомных ансамблей, в которых роли отдельных атомов взаимозаменяемы. В таком ансамбле имеется возможность микро-причинности: траекторию каждого кванта амплитуды можно определить однозначно.
An ensemble of identical two level atoms in dark state neither adsorbs nor emits photons due to destructive interference. Dark states have numerous applications. It can be used for the source of energy for nano-devices; the space of dark states is decoherence free and can serve as the carrier for the fault tolerant quantum computations, etc. Since a dark state does not interact with the electromagnetic field it is an eigenstate of Tavis-Cummings Hamiltonian and the preparation of such states requires the exit from this model. We show how to prepare a dark state by the photon pumping and drain from the optical cavity with two atoms, one from which has Stark or Zeeman splitting of energy levels. This splitting is removed before photon drain from the cavity. The dark state yield after one such cycle has the order of energy level splitting. We show the scheme of the experiment, in which such cycles repeat until the dark state is produced with high probability and the results of its computer simulation. The structure of dark states is briefly discussed.
Decoherence-free subspaces allow for the preparation of coherent and entangled qubits for quantum computing. Decoherence can be dramatically reduced, yet dissipation is an integral part of the scheme in generating stable qubits and manipulating them via one- and two-bit gate operations. How this works can be understood by comparing the system with a three-level atom exhibiting a macroscopic dark period. In addition, a dynamical explanation is given for a scheme based on atoms inside an optical cavity in the strong-coupling regime and we show how spontaneous emission by the atoms can be highly suppressed.
Fock-state lattices (FSLs) are becoming an emerging research hotspot in quantum physics, not only because the FSLs provide a new perspective for studying atom-field interactions, but also because they build a connection between quantum optics and condensed matter physics. Because of the multiple transition paths in the lattices, an inherent quantum interference effect exists in these systems, and hence finding new quantum-coherent phenomena and exploiting their applications become a significant and desired task in this field. In this work, we study the dark-state effect in the FSLs generated by the multimode Jaynes-Cummings (JC) models. By considering the FSLs in certain excitation-number subspaces, we study the dark states with respect to the states associated with the atomic excited state using the arrowhead-matrix method. We find that dark-state subspaces exist with dimensions determined by the number of orthogonal dark states. When the dimension is greater than one, the forms of these dark-state bases are not unique. Further, we obtain the number and form of the orthogonal dark states in the two-, three-, and four-mode JC models. In addition, we find that for a general N -mode JC model, there are C N + n − 2 N − 2 orthogonal dark states in the n -excitation subspace. We also build the relationship between the dark states and dark modes. Our work paves the way for exploring quantum optical effects and quantum information processing based on the FSLs.