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arXiv:1510.00700 · Physical Review A

Quantum state transfer in a disordered one-dimensional lattice

Sahel Ashhab

Published Dec 3, 2015• 36 citations
arXivHTMLPDF

Abstract

We investigate the effect of disorder on the transfer of quantum states across a one-dimensional lattice with varying levels of control resources. We find that the application of properly designed control signals, even when applied only to the two ends of the lattice, allows perfect state transfer up to disorder strengths that would not allow a generic quantum state to propagate the length of the lattice. At sufficiently large disorder strengths, however, the local control signals fail to send the quantum state from one end of the system to the other end. Our results shed light on the interplay between disorder and controlled transport in one-dimensional systems.

DOI
10.1103/physreva.92.062305

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We investigate the effect of disorder on the transfer of quantum states across a one-dimensional lattice with varying levels of control resources. We find that the application of properly designed control signals, even when applied only to the two ends of the lattice, allows perfect state transfer up to disorder strengths that would not allow a generic quantum state to propagate the length of the lattice. At sufficiently large disorder strengths, however, the local control signals fail to send the quantum state from one end of the system to the other end. Our results shed light on the interplay between disorder and controlled transport in one-dimensional systems.
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Abstract Particle transport and localization phenomena in condensed-matter systems can be modeled using a tight-binding lattice Hamiltonian. The ideal experimental emulation of such a model utilizes simultaneous, high-fidelity control and readout of each lattice site in a highly coherent quantum system. Here, we experimentally study quantum transport in one-dimensional and two-dimensional tight-binding lattices, emulated by a fully controllable 3 × 3 array of superconducting qubits. We probe the propagation of entanglement throughout the lattice and extract the degree of localization in the Anderson and Wannier-Stark regimes in the presence of site-tunable disorder strengths and gradients. Our results are in quantitative agreement with numerical simulations and match theoretical predictions based on the tight-binding model. The demonstrated level of experimental control and accuracy in extracting the system observables of interest will enable the exploration of larger, interacting lattices where numerical simulations become intractable.
The interplay between disorder and interactions has a large impact on the properties of quantum systems. Although it is present in any real physical system, disorder is difficult to control, to tune, and therefore to study. Even more challenging is the investigation of the combined effect of disorder and interactions. While non-interacting particles can be localized by disorder, interactions can support superfluidity, a state of matter normally impervious to disorder. The complex interplay between the two can lead to new, unconventional phases, still not completely understood neither in theory nor in experiments. Ultracold atoms in optical lattices represent an ideal test-bed to study the physical properties of disordered systems.
The ability to transfer quantum information from one location to another with high probability is of central importance to quantum information science. Unfortunately, for the simplest system of a uniform chain (a spin chain or a particle in a one-dimensional lattice), the state transfer time grows exponentially in the chain length NNN at fixed transfer probability. In this work we show that the addition of an impurity near each end point, coupled to the uniform chain with strength www, is sufficient to ensure efficient and high-probability state transfer. An eigenstate localized in the vicinity of the impurity can be tuned into resonance with chain-extended states by adjusting $w(N)\ensuremath{\propto}{N}^{1/2}$; the resulting avoided crossing yields resonant eigenstates with large amplitudes on the chain end points and approximately equidistant eigenvalues. The state transfer time scales as $t\ensuremath{\propto}{N}^{3/2}$, and its transfer probability PPP approaches unity in the thermodynamic limit $N\ensuremath{\rightarrow}\ensuremath{\infty}$; the error scales as $1\ensuremath{-}P\ensuremath{\propto}{N}^{\ensuremath{-}1}$. Thus, with the addition of two impurities, asymptotically perfect efficient state transfer with a uniform chain is possible even in the absence of external control.
We analyze the interplay of disorder and long-range hopping in a paradigmatic one dimensional model of quantum transport. While typically the current is expected to decrease as the disorder strength increases due to localization effects, in systems with infinite range hopping it was shown in Chavez et al, Phys. Rev. Lett. 126, 153201 (2021), that the current can increase with disorder in the Disorder-Enhanced-Transport (DET) regime. Here, by analyzing models with variable hopping range decaying as 1/rα1/r^α1/rα with the distance rrr among the sites, we show that the DET regime is a general feature of long-range hopping systems and it occurs, not only in the strong long-range limit α<1α<1α<1 but even for weak long-range 1≤α≤31 \le α\le 31≤α≤3. Specifically, we show that, after an initial decrease, the current grows with the disorder strength until it reaches a local maximum. Both disorder thresholds at which the DET regime starts and ends are determined. Our results open the path to understand the effect of disorder on transport in many realistic systems where long range hopping is present.
We analyze the interplay of disorder and long-range hopping in a paradigmatic one-dimensional model of quantum transport. While typically the current is expected to decrease as the disorder strength increases due to localization effects, in systems with infinite range hopping, it was shown in Chavez et al. [Phys. Rev. Lett. 126, 153201 (2021)] that the current can increase with disorder in the disorder-enhanced-transport (DET) regime. Here, by analyzing models with variable hopping range decaying as 1/rα with the distance r among the sites, we show that the DET regime is a general feature of long-range hopping systems and it occurs, not only in the strong long-range limit α < 1 but even for weak long range 1 < α < 3. Specifically, we show that, after an initial decrease, the current grows with the disorder strength until it reaches a local maximum. Both disorder thresholds at which the DET regime starts and ends are determined. Our results open the path to understand the effect of disorder on transport in many realistic systems where long-range hopping is present.