Quantum Computation with Trapped Ions in an Optical Cavity

Abstract

Two-qubit logical gates are proposed on the basis of two atoms trapped in a cavity setup. Losses in the interaction by spontaneous transitions are efficiently suppressed by employing adiabatic transitions and the Zeno effect. Dynamical and geometrical conditional phase gates are suggested. This method provides fidelity and a success rate of its gates very close to unity. Hence, it is suitable for performing quantum computation.One of the main obstacles in realizing a quantum computer (QC) is decoherence resulting from the coupling of the system with the environment. There are theoretical proposals for models which avoid decoherence [1][2][3][4]. For this purpose decoherence-free subspaces (DFS) have been proposed in the literature for performing QC [5][6][7]. While they are easy to construct in the case of a single qubit, they are more complicated for the case of an externally controlled multipartite system. Their main decoherence channel is the "bus" that couples the different subsystems and is usually strongly perturbed by the environment. In the case of an ion trap the bus is the common vibrational mode which is subject to continuous heating. In the case of cavity QED the bus is a cavity mode which may leak to the environment. Additionally the cavity couples to an excited state of the atom that shows spontaneous emission. To avoid these phenomenon it is most convenient to transfer population by virtually populating the bus [3,4,[8][9][10]. Here we present a model with atoms in an optical cavity that bypasses the decoherence problem with, in principle, arbitrarily large fidelity and success rate.Atomic levels of the two atoms and laser and cavity couplings with their detunings. The qubits 1, 2 and the auxiliary states |σ are depicted.The system presented here consists of two four-level atoms fixed inside an optical cavity, Fig. 1. This can be achieved by, for example, having trapped ions in a cavity with its axis perpendicular to the ionic chain. It is assumed that the atoms have the lower states, |0 , |1 and |σ , which could be represented by different hyperfine levels or Zeeman levels, and an excited state |2 coupled individually to each ground state by laser radiation with different polarizations or frequencies. The atoms interact with each other via the common cavity radiation field.Our goal is to perform QC in such a way that coherent evolution can be performed even for high loss rates, κ, of the cavity and relatively large decay rates, Γ, of the excited atomic states. This is achieved by employing an adiabatic procedure that keeps the cavity empty and the excited state of the atoms depopulated. Information is transfered by virtual population of these decohering atomic and cavity states. The entangling adiabatic transfer of population between ground state levels occurs by slowly varying the Rabi frequencies of the lasers in a counterintuitive temporal sequence, similarly to the well-known STIRAP process for Λ systems, but now it is performed in the space spanned by the tensor product states of the two ato...

Realizing quantum controlled phase flip through cavity QED

“…Quantum computation based on cavity quantum electrodynamics (QED) [1,2] attracts persistent interest in experimental realization [3,4,5,6,7]. In theory, cavity-QED with longlived states and high-Q cavities thus provides a promising tool for creating entanglement and superposition, and also for implementation of quantum computing algorithms.…”

“…In theory, cavity-QED with longlived states and high-Q cavities thus provides a promising tool for creating entanglement and superposition, and also for implementation of quantum computing algorithms. In a number of different schemes, quantum information usually can be represented by states of photons [3,4] or atomic/ionic states [5,6,7]. In a classical quantum computation scheme based on cavity-QED of Ref.…”

Three Different Manifestations of the Quantum Zeno Effect

“…added to (36) in the three-level scheme (35)- (37). One obtains again, in the N → ∞ limit, the decomposition H 1 ⊕ H 2 .…”

“…The numerical figures we have given are realistic and the Hamiltonian (54) is a good approximation of the decay process at short (for the physical meaning of "short", see [4,34,35]) and intermediate times (it is not valid for very large times, where a power law should appear). Related interesting proposals, making use of kicks or continuous coupling in cavity QED, can be found in [36]. We stress, once again, that the key issue to address is that of the physically relevant numerical figures and timescales.…”

Vacuum-induced Stark shifts for quantum logic using a collective system in a high-quality dispersive cavity

“…We note that we work strictly with qubits and do not use any additional levels for the logic operation [19]. The use of additional levels [20,21,22,23,24,25,26] may lead to additional sources of decoherence either due to local environment or due to the fields which are used to address such levels.…”