Adopting the framework of two-coupled superconducting charges model, we discussed the information entropy of two qubits initially prepared in a mixed state and allowed to interact with their environment. The impact of the different parameters of the system is explicitly investigated. Present calculations show that strong mutual entropy is obtained for a long interaction time when the two qubits are initially in a mixed state with the environment switched off. We have identified a class of two-qubit states that have a rich dynamics when the deviation between the characteristic energies of the quabits becomes minimum. It was found that the total correlation decreases abruptly to zero in a finite time due to the influence of the strong environment.
We have investigated the decoherence of quantum states in two Al/AlOx/Al Cooper-pair boxes coupled to lumped element superconducting LC resonators. At 25 mK, the first qubit had an energy relaxation time T1 that varied from 30 us to 200 us between 4 and 8 GHz and displayed an inverse correlation between T1 and the coupling to the microwave drive line. The Ramsey fringe decay times T2* were in the 200-500 ns range while the spin echo envelope decay times Techo varied from 2.4-3.3 us, consistent with 1/f charge noise with a high frequency cutoff of 0.2 MHz. A second Cooper-pair box qubit with si…
We study the behaviour of charge oscillations in Superconducting Cooper Pair Boxes weakly interacting with an environment. We found that, due to the noise and dissipation induced by the environment, the stability properties of these nanodevices differ according to whether the charge oscillations are interpreted as an effect of macroscopic quantum coherence, or semiclassically in terms of the Gross-Pitaevskii equation. More specifically, occupation number states, used in the quantum interpretation of the oscillations, are found to be much more unstable than coherent ones, typical of the semicla…
Charge fluctuations from gate bias and background traps severely limit the performance of a charge qubit in a Cooper-pair box (CPB). Here we present an experimentally realizable method to control the decoherence effects of these charge fluctuations using two strongly capacitively coupled CPBs. This coupled-box system has a low-decoherence subspace of two states. Our results show that the inter-box Coulomb correlation can help significantly suppress decoherence of this two-level system, making it a promising candidate as a logical qubit, encoded using two CPBs.
We consider an array of Cooper Pair Boxes, each of which is coupled to a superconducting reservoir by a capacitive tunnel junction. We discuss two effects that probe not just the quantum nature of the islands, but also of the superconducting reservoir coupled to them. These are analogues to the well-known quantum optical effects `superradiance,' and `revival.' When revival is extended to multiple systems, we find that `entanglement revival' can also be observed. In order to study the above effects, we utilise a highly simplified model for these systems in which all the single-electron energy e…
If an atom is able to exhibit macroscopic dark periods, or electron shelving, then a driven system of two atoms has three types of fluorescence periods (dark, single and double intensity). We propose to use the average durations of these fluorescence types as a simple and easily accessible indicator of cooperative effects. As an example we study two dipole-interacting V systems by simulation techniques. We show that the durations of the two types of light periods exhibit marked separation-dependent oscillations and that they vary in phase with the real part of the dipole-dipole coupling consta…
The mutual dipole-dipole interaction of atoms in a trap can affect their fluorescence. Extremely large effects were reported for double jumps between different intensity periods in experiments with two and three Ba^+ ions for distances in the range of about ten wave lengths of the strong transition while no effects were observed for Hg^+ at 15 wave lengths. In this theoretical paper we study this question for configurations with three and four levels which model those of Hg^+ and Ba^+, respectively. For two systems in the Hg^+ configuration we find cooperative effects of up to 30% for distance…
We investigate the action of time dependent detunings upon the excitation inversion of a Cooper pair box interacting with a nanomechanical resonator. The method employs the Jaynes-Cummings model with damping, assuming different decay rates of the Cooper pair box and various fixed and t-dependent detunings. It is shown that while the presence of damping plus constant detunings destroy the collapse/revival effects, convenient choices of time dependent detunings allow one to reconstruct such events in a perfect way. It is also shown that the mean excitation of the nanomechanical resonator is more…
We investigate the quantum entropy, its power spectrum, and the excitation inversion of a Cooper pair box interacting with a nanomechanical resonator, the first initially prepared in its excited state, the second prepared in a "cat"-state. The method uses the Jaynes-Cummings model with damping, with different decay rates of the Cooper pair box and distinct detuning conditions, including time dependent detunings. Concerning the entropy, it is found that the time dependent detuning turns the entanglement more stable in comparison with previous results in literature. With respect to the Cooper pa…
We present an experimentally realizable stabilized charge pumping scheme in a linear array of Cooper-pair boxes. The system design intrinsically protects the pumping mechanism from severe errors, especially current reversal and spontaneous charge excitation. The quantum Zeno effect is implemented to further diminish pumping errors. The characteristics of this scheme are considered from the perspective of improving the current standard. Such an improvement bears relevence to the closure of the so-called measurement triangle (see D. Averin [Nature 434, 285 (2005)]).
Cooperative effects in the fluorescence of two dipole-interacting atoms, with macroscopic quantum jumps (light and dark periods), are investigated. The transition rates between different intensity periods are calculated in closed form and are used to determine the rates of double jumps between periods of double intensity and dark periods, the mean duration of the three intensity periods and the mean rate of their occurrence. We predict, to our knowledge for the first time, cooperative effects for double jumps, for atomic distances from one and to ten wave lengths of the strong transition. The …
We consider the Jaynes-Cummings model describing the interaction of a Cooper pair box (CPB) and a nanoresonator (NR) in the presence of a Kerr medium and losses The evolution of the entropy of both subsystems and the CPB population inversion were calculated numerically. It is found that these properties increase when the NR frequency is time-dependent, even in the presence of losses; the effect is very sensitive to detuning and disappears in the resonant regime. The roles played by the losses affecting the CPB and the NR are also compared.
First solid state quantum computer was built using transmons (cooper pair boxes). The operation of the computer is limited because of using a number of the rigit cooper boxes working with fixed frequency at temperatures of superconducting material. Here, we propose a novel architecture of quantum computer based on a flexible wire circuit of many coupled quantum nodes containing controlled atomic (molecular) ensembles. We demonstrate wide opportunities of the proposed computer. Firstly, we reveal a perfect storage of external photon qubits to multi-mode quantum memory node and demonstrate a rev…
We investigate the cooperative behavior of regular monolayers of driven two-level dipoles, using classical electrodynamics simulations. The dipolar response results from the interference of many cooperative eigenmodes, each frequency-shifted from the single resonant dipole case, and with a modified lifetime, due to the interactions between dipoles. Of particular interest is the kagome lattice, where the semiregular geometry permits simultaneous excitation of two dominant modes, one strongly subradiant, leading to an electromagnetically-induced-transparency-like interference in a two-level syst…
Using the standard Hamiltonian of the BCS theory, we show that in an ensemble of interacting fermions with the spin 1/2 there exist coherent states $|NC>$, which nullify the Hamiltonian of the interparticle interaction (scattering). These states have an analogy with the well-known in quantum optics the coherent population trapping (CPT) effect. The structure of these CPT-like states corresponds to Cooper pairs with the total spin $S$=1. The found states have a huge degree of degeneracy and carry a macroscopic magnetic moment, that allows us to construct a new model of the magnetism connected w…
We describe an efficient numerical method for simulating the dynamics of interacting spin ensembles in the presence of dephasing and decay. The method builds on the discrete truncated Wigner approximation for isolated systems, which combines the mean-field dynamics of a spin ensemble with a Monte Carlo sampling of discrete initial spin values to account for quantum correlations. Here we show how this approach can be generalized for dissipative spin systems by replacing the deterministic mean-field evolution by a stochastic process, which describes the decay of coherences and populations while …
We describe an assembly of N Cooper-pair boxes (CPB) contained in a single mode cavity. In the dispersive regime, the correlation between the cavity field and each Cooper-pair box results in an effective interaction between CPBs that can be used to dynamically generate maximally entangled states. With only collective manipulations, we show how to create maximally entangled quantum states and how to use these states to reach the Heisenberg limit in the determination of a spectroscopy frequency. This scheme can be applied to other types of superconducting qubits.
We consider an array of coupled optical cavities, each containing a multi-atom ensemble. We show that the nonlinearity inherent in the cooperative dynamics of the atoms in each ensemble coupled to the respective cavity field allows for the formation of solitary waves. Such a prediction can be tested in state-of-the-art semiconducting photonic-crystal microcavities with embedded impurities.
The speed of computations is investigated by means of the orthogonality speed for a charged qubit interacting with a single cavity field prepared initially in a Fock state or Binomial state. We observe that the rate of the computational speed is related to the number of photons inside the cavity. Moreover, we show that the qubit-field coupling plays an opposite role, where the speed of computations is decreased as the coupling is increased. We suggest using the number of photons in the field as a control parameter to improve the speed of computations.
We examined properties of a Josephson-junction system composed of two coupled Cooper-pair boxes (charge qubits) as a candidate for observation of quantum holonomies. We construct a universal set of transformations in a two-fold degenerate ground state, and discuss the effects of noise in the system.
Pairing is the fundamental requirement for fermionic superfluidity and superconductivity. To understand the mechanism behind pair formation is an ongoing challenge in the study of many strongly correlated fermionic systems. Cooper pairs are the key ingredient to BCS theory as the microscopic explanation of conventional superconductivity. They form between particles of opposite spin and momentum at the Fermi surface of the system. Here, we directly observe Cooper pairs in a mesoscopic two-dimensional Fermi gas. We apply an imaging scheme that enables us to extract the full in-situ momentum dist…
We consider a gas of attractively interacting cold Fermionic atoms which are manipulated by laser light. The laser induces a transition from an internal state with large negative scattering length to one with almost no interactions. The process can be viewed as a tunneling of atomic population between the superconducting and the normal states of the gas. It can be used to detect the BCS-ground state and to measure the superconducting order parameter.
We study photon emission by an ensemble of two-level systems, with strong inhomogeneous broadening and coupled to a cavity mode whose frequency has linear time-dependence. The analysis shows that, regardless the distribution of energy level splittings, a sharp phase transition occurs between the weak and strong cooperative emission phases near a critical photonic frequency sweeping rate. The associated scaling exponent is determined. We suggest that this phase transition can be observed in an ensemble of negatively charged NV centers in diamond interacting with a microwave half-wavelength cavi…
