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arXiv:1912.12488 · Physical Review Applied

Quantum Emulation of Coherent Backscattering in a System of Superconducting Qubits

Ana Laura Gramajo, Dan Campbell, Bharath Kannan, David K. Kim, Alexander J. Melville, Bethany M. Niedzielski, Jonilyn Yoder, María José Sánchez, Daniel Domínguez, Simon Gustavsson, William D. Oliver

Published Jul 16, 2020• 6 citations
arXivHTMLPDF

Abstract

In condensed matter systems, coherent backscattering and quantum interference in the presence of time-reversal symmetry lead to well-known phenomena, such as weak localization (WL) and universal conductance fluctuations (UCFs). Here we use multipass Landau-Zener transitions at the avoided crossing of a highly coherent superconducting qubit to emulate these phenomena. The average and standard deviations of the qubit transition rate exhibit a dip and peak when the driving waveform is time-reversal symmetric, analogous to WL and UCFs, respectively. The higher coherence of this qubit enabled the realization of both effects, in contrast to the earlier work by Gustavsson et al. [Phys. Rev. Lett. 110, 016603 (2013)], who successfully emulated UCFs, but did not observe WL. This demonstration illustrates the use of nonadiabatic control to implement quantum emulation with superconducting qubits.

DOI
10.1103/physrevapplied.14.014047

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In condensed matter systems, coherent backscattering and quantum interference in the presence of time-reversal symmetry lead to well-known phenomena, such as weak localization (WL) and universal conductance fluctuations (UCFs). Here we use multipass Landau-Zener transitions at the avoided crossing of a highly coherent superconducting qubit to emulate these phenomena. The average and standard deviations of the qubit transition rate exhibit a dip and peak when the driving waveform is time-reversal symmetric, analogous to WL and UCFs, respectively. The higher coherence of this qubit enabled the realization of both effects, in contrast to the earlier work by Gustavsson et al. [Phys. Rev. Lett. 110, 016603 (2013)], who successfully emulated UCFs, but did not observe WL. This demonstration illustrates the use of nonadiabatic control to implement quantum emulation with superconducting qubits.
In condensed matter systems, coherent backscattering and quantum interference in the presence of time-reversal symmetry lead to well-known phenomena, such as weak localization (WL) and universal conductance fluctuations (UCFs). Here we use multipass Landau-Zener transitions at the avoided crossing of a highly coherent superconducting qubit to emulate these phenomena. The average and standard deviations of the qubit transition rate exhibit a dip and peak when the driving waveform is time-reversal symmetric, analogous to WL and UCFs, respectively. The higher coherence of this qubit enabled the realization of both effects, in contrast to the earlier work by Gustavsson et al. [Phys. Rev. Lett. 110, 016603 (2013)], who successfully emulated UCFs, but did not observe WL. This demonstration illustrates the use of nonadiabatic control to implement quantum emulation with superconducting qubits.
In the presence of time-reversal symmetry, quantum interference gives strong corrections to the electric conductivity of disordered systems. The self-interference of an electron wave function traveling time-reversed paths leads to effects such as weak localization and universal conductance fluctuations. Here, we investigate the effects of broken time-reversal symmetry in a driven artificial two-level system. Using a superconducting flux qubit, we implement scattering events as multiple Landau-Zener transitions by driving the qubit periodically back and forth through an avoided crossing. Interference between different qubit trajectories gives rise to a speckle pattern in the qubit transition rate, similar to the interference patterns created when coherent light is scattered off a disordered potential. Since the scattering events are imposed by the driving protocol, we can control the time-reversal symmetry of the system by making the drive waveform symmetric or asymmetric in time. We find that the fluctuations of the transition rate exhibit a sharp peak when the drive is time symmetric, similar to universal conductance fluctuations in electronic transport through mesoscopic systems.
Superconducting qubits already demonstrated potential in emulating coherent back scattering or weak localization (WL) and tunnelling phenomena however, in a real multipath system they have not been verified yet.Here we show how a double-path system can be emulated by a quantum device through construction of multiple scattering centers in closed paths (detune boxes) and tunnel barriers with a large return probability (Pr) of electrons. Incorporation of such arrangements of tunnel barriers can add an extra geometric phase and demonstrate Aharonov-Bohm type oscillations (phi)0 and (phi/2)0 in a ring and a tube, respectively. A combination of inter and intra layer tunnelling in a double-path circuit creates a phase reversal and subsequently weak anti-localization (WAL) effect with a long coherence time. Finally, angle dependence of Pr firmly establishes stability of the two-path circuit which is also associated with a phase reversal due to the inter-path resonance.
We investigate the effect of broken time reversal symmetry in flux qubits driven by a biharmonic magnetic flux signal with a phase lag. In the regime of large relaxation times, we explicitly compute the transition rate between the ground and the excited state, accounting for decoherence as a classical noise. Through a direct analogy between interference effects at the avoided level crossing and scattering events in weakly disordered electronic mesoscopic systems, the transition rate plays the role of an effective transmittance while the phase lag acts as a time reversal control parameter. Clear signatures of both weak localization and conductance fluctuations-like effects are predicted. Their behavior is studied as a function of the coherence rate, and a comparison with recent experimental results is performed. Our study shows that it is decoherence, and not the driving protocol, what limits the experimental detection of weak localization effects.
Reciprocity is a universal principle that has a profound impact on many areas of physics. A fundamental phenomenon in condensed-matter physics, optical physics, and acoustics, arising from reciprocity, is the constructive interference of quantum or classical waves which propagate along time-reversed paths in disordered media, leading to, for example, weak localization and metal-insulator transition. Previous studies have shown that such coherent effects are suppressed when reciprocity is broken. Here we experimentally show that by tuning a nonreciprocal phase we can coherently control complex coherent phenomena, rather than simply suppress them. In particular, we manipulate coherent backscattering of light, also known as weak localization. By utilizing a magneto-optical effect, we control the interference between time-reversed paths inside a multimode fiber with strong mode mixing, observe the optical analog of weak antilocalization, and realize a continuous transition from weak localization to weak antilocalization. Our results may open new possibilities for coherent control of waves in complex systems.
A new regime of coherent quantum dynamics of a qubit is realized at low driving frequencies in the strong driving limit. Coherent transitions between qubit states occur via the Landau-Zener process when the system is swept through an energy-level avoided crossing. The quantum interference mediated by repeated transitions gives rise to an oscillatory dependence of the qubit population on the driving-field amplitude and flux detuning. These interference fringes, which at high frequencies consist of individual multiphoton resonances, persist even for driving frequencies smaller than the decoherence rate, where individual resonances are no longer distinguishable. A theoretical model that incorporates dephasing agrees well with the observations.