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.
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.
Ensemble of identical two level atoms in dark state neither adsorbs nor emits photons due to destructive interference. It can be used for the source of energy for nano-devices. In Tavis-Cummings cavity the change of light-atom coupling cannot destroy the dark state. We propose the method of dark states preparation based on 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 computer simulation.
Quantum mechanics allows for light-matter setups that hold excitations without releasing them as light. Arising from destructive interference processes, they are best seen in a Tavis-Cummings-like setup where two-level atoms (or qubits) are placed within a lossy cavity. If the system is initialized with some qubits excited and some in the ground state, there is a non-zero probability that no photons will be emitted. This can be framed as a Stern-Gerlach measurement, with a detector to measure if one or more photons leave the cavity. If no photons are detected, the qubits collapse onto a dark state. This can be viewed as heralding of a dark state based on zero photon detection. Building upon this idea, we propose a protocol to measure the number of independent dark states. Moreover, we show that this quantity is robust to arbitrary levels of disorder in the qubit-photon coupling constants. We then discuss a phase transition where the number of dark states plays the role of an order parameter. This provides an exciting example of a phase transition that is completely insensitive to disorder.
Abstract Quantum mechanics allows for light-matter setups that hold excitations without releasing them as light. Arising from destructive interference processes, they are best seen in a Tavis-Cummings-like setup where two-level atoms (or qubits) are placed within a lossy cavity. If the system is initialized with some qubits excited and some in the ground state, there is a non-zero likelihood of no photons being emitted. This can be framed as a Stern-Gerlach measurement, with a detector to measure if one or more photons leave the cavity. If no photons are detected, the qubits collapse onto a dark state. This can be viewed as heralding of a dark state based on zero photon detection. Building upon this idea, we propose a protocol to measure the number of independent dark states. Remarkably, we show that this quantity is robust to arbitrary levels of disorder in the qubit-photon coupling constants. This provides a rare example of an observable that remains unchanged with any amount of disorder. We then discuss a phase transition where the number of dark states plays the role of an order parameter. This provides a rare example of a phase transition that is completely insensitive to disorder.
We propose quantum protection circuit (quantum lock), based on dark states of ensembles of two-level atoms in optical cavity. The secret key is the splitting of atoms into pairs, and publicly accessible part of the lock is the tensor product of EPR singlets, corresponding to the given splitting. To open the lock one must move synchronously pairs of atoms from the correct splitting to the other cavity; the lock will open if atoms do not emit photons. This scheme has perfect secrecy: it is impossible to hack it, even with effective solutions of any classical computational problems, in contrast to the RSA scheme. The method of obtaining dark states through Stark shift of atomic excitation energy is also proposed. This scheme makes possible to create secret keys of a few tens of atoms that is sufficient for the most practical applications.
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.
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.