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arXiv:1301.2991 · Physical Review A

Nonadiabatic quantum state control of many bosons in few wells

Malte C. Tichy, Mads Kock Pedersen, Klaus Mølmer, Jacob Friis Sherson

Published Jun 24, 2013• 12 citations
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Abstract

We present a fast scheme for arbitrary unitary control of interacting bosonic atoms in a double well. Assuming fixed interwell tunneling rate and intrawell interaction strength, we control the many-atom state by a discrete sequence of shifts of the single-well energies. For strong interactions, resonant tunneling transitions implement beam-splitter U(2) rotations among atom number eigenstates, which can be combined and, thus, permit full controllability. By numerically optimizing such sequences of couplings at avoided level crossings, we extend the realm of full controllability to a wide range of realistic interaction parameters, while we remain in the simple control space. We demonstrate the efficiency and the high achievable fidelity of our proposal with nonadiabatic population transfer, NOON-state creation, a cnot gate, and a transistorlike, conditional evolution of several atoms.

DOI
10.1103/physreva.87.063422

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We present a fast scheme for arbitrary unitary control of interacting bosonic atoms in a double well. Assuming fixed interwell tunneling rate and intrawell interaction strength, we control the many-atom state by a discrete sequence of shifts of the single-well energies. For strong interactions, resonant tunneling transitions implement beam-splitter U(2) rotations among atom number eigenstates, which can be combined and, thus, permit full controllability. By numerically optimizing such sequences of couplings at avoided level crossings, we extend the realm of full controllability to a wide range of realistic interaction parameters, while we remain in the simple control space. We demonstrate the efficiency and the high achievable fidelity of our proposal with nonadiabatic population transfer, NOON-state creation, a cnot gate, and a transistorlike, conditional evolution of several atoms.
We suggest a simple scheme for creating a NOON state of repulsively interacting Bose atoms in the double-well potential. The protocol consists of two steps. First, by setting atom-atom interactions to zero, the system is driven to the upper excited state. Second, the interactions are slowly increased and, simultaneously, the interwell tunneling is decreased to zero. We analyze fidelity of the final state to the NOON state depending on the number of atoms, ramp rate, and fluctuations of the system parameters. It is shown that for a given fidelity the ramp rate scales algebraically with the number of atoms.
We investigate few-boson tunneling in a one-dimensional double well, covering the full crossover from weak interactions to the fermionization limit of strong correlations. Based on exact quantum-dynamical calculations, it is found that the tunneling dynamics of two atoms evolves from Rabi oscillations to correlated pair tunneling as we increase the interaction strength. Near the fermionization limit, fragmented-pair tunneling is observed and analyzed in terms of the population imbalance and two-body correlations. For more atoms, the tunneling dynamics near fermionization is shown to be sensitive to both atom number and initial configuration.
We propose a scheme to implement single-qubit operations for singlet-triplet qubits located in an isolated double-well potential with fixed inter-site tunneling when superexchange interactions predominate. Arbitrary single-qubit gates can be realized by a sequence composed of two elementary operations which can be switched between different parameter regimes by adjusting slightly the relative energy bias of trapped atoms in each sub-well site. The experimental feasibility of the strategy and the fidelity of basic rotation operations are also analyzed.
We investigate theoretically the generation of microscopic atomic NOON states, corresponding to the coherent $|N,0\ensuremath{\rangle}+|0,N\ensuremath{\rangle}$ superposition with $N\ensuremath{\sim}5$ particles, via collective tunneling of interacting ultracold bosonic atoms within a symmetric double-well potential in the self-trapping regime. We show that a periodic driving of the double well with suitably tuned amplitude and frequency parameters allows one to substantially boost this tunneling process without altering its collective character. The timescale to generate the NOON superposition, which corresponds to half the tunneling time and would be prohibitively large in the undriven double well for the atomic populations considered, can thereby be drastically reduced, which renders the realization of NOON states through this protocol experimentally feasible. Resonance- and chaos-assisted tunneling are identified as key mechanisms in this context. A quantitative semiclassical evaluation of their impact on the collective tunneling process allows one to determine the optimal choice for the driving parameters in order to generate those NOON states as fast as possible.
Abstract Quantum gates can be implemented adiabatically and nonadiabatically. Many schemes used at least two sequentially implemented gates to obtain an arbitrary one-qubit gate. Recently, it has been shown that nonadiabatic gates can be realized by single-shot implementation. It has also been shown that quantum gates can be implemented with controlled adiabatic evolutions. In this paper, we combine the advantage of single-shot implementation with controlled adiabatic evolutions to obtain controlled nonadiabatic evolutions. We also investigate the robustness to different types of errors. We find that the fidelity is close to unity for realistic decoherence rates.
We present an analytical framework for stabilizing second-order correlated tunneling of two spin-orbit-coupled bosons in a periodically driven non-Hermitian double-well potential. By combining Floquet theory with multiple-scale asymptotic analysis, we derive effective second-order dynamics and exact quasienergy spectra in the strongly interacting regime. Our analysis reveals distinct stability mechanisms for three fundamental tunneling channels: interwell spin-conserving, interwell spin-flipping, and intrawell spin-flipping. For balanced gain and loss, we identify discrete, well-defined parameter regions where stable pair tunneling emerges, with the spin-flipping channel exhibiting a characteristic symmetry absent in its spin-conserving counterpart. Under unbalanced gain-loss conditions, stability is achieved only when the gain and loss coefficients satisfy specific parametric relations, enabling dissipation-controlled tunneling. Most notably, stable intrawell spin-flipping, while inherently unstable for an initial Fock state, becomes accessible when the system is prepared in a coherent superposition state, thereby revealing that initial-state coherence can serve as a control parameter for dynamical stability in non-Hermitian systems. These results expand the possibilities for controlling correlated tunneling in many-body systems with engineered dissipation.