Programmable Interference between Two Microwave Quantum Memories

Open Access

Programmable Interference between Two Microwave Quantum Memories

Yvonne Y. Gao, Brian J. Lester, Yaxing Zhang, Chen Wang, Serge Rosenblum, Luigi Frunzio, Liang Jiang, S. M. Girvin, and Robert J. Schoelkopf

Phys. Rev. X 8, 021073 – Published 21 June 2018

Abstract

Interference experiments provide a simple yet powerful tool to unravel fundamental features of quantum physics. Here we engineer a driven, time-dependent bilinear coupling that can be tuned to implement a robust $50 ∶ 50$ beam splitter between stationary states stored in two superconducting cavities in a three-dimensional architecture. With this, we realize high-contrast Hong-Ou-Mandel interference between two spectrally detuned stationary modes. We demonstrate that this coupling provides an efficient method for measuring the quantum state overlap between arbitrary states of the two cavities. Finally, we showcase concatenated beam splitters and differential phase shifters to implement cascaded Mach-Zehnder interferometers, which can control the signature of the two-photon interference on demand. Our results pave the way toward implementation of scalable boson sampling, the application of linear optical quantum computing protocols in the microwave domain, and quantum algorithms between long-lived bosonic memories.

Received 23 February 2018
Revised 27 April 2018

DOI:https://doi.org/10.1103/PhysRevX.8.021073

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Boson sampling Quantum interference effects Quantum memories

Quantum Information, Science & TechnologyAtomic, Molecular & Optical

Authors & Affiliations

Yvonne Y. Gao^1,*, Brian J. Lester¹, Yaxing Zhang¹, Chen Wang², Serge Rosenblum¹, Luigi Frunzio¹, Liang Jiang¹, S. M. Girvin¹, and Robert J. Schoelkopf^1,†

¹Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06520, USA and Yale Quantum Institute, Yale University, New Haven, Connecticut 06511, USA
²University of Massachusetts, Amherst, Massachusetts 01003-9337, USA

^*Corresponding author. yvonne.gao@yale.edu
^†Corresponding author. robert.schoelkopf@yale.edu

Popular Summary

Interference between particles is one of the simplest and yet most elegant demonstrations of quantum mechanics. It provides insights into fundamental scientific problems and enables technological applications such as quantum computing and cryptography. Pioneering experiments often used optical photons, which interfere readily through simple beam splitters. However, studying more complex interference phenomena requires the ability to create, manipulate, and measure arbitrary quantum states. While these tasks are challenging for photons flying along an optical fiber, high-quality experiments can be performed on trapped particles. We show that it is possible to combine the best of both worlds in a single system where we have the ability to prepare and control exotic quantum states, as well as the capability to switch on a robust and tunable coupling between them.

We engineered a time-dependent bilinear coupling that can be tuned to implement a robust $50 ∶ 50$ beam splitter between stationary states stored in two superconducting cavities. With this, we realize an interesting two-photon interference where the photons always exit in pairs from a single, albeit random, port of the beam splitter. We also efficiently probe the quantum state overlap between two multiphoton states. Lastly, we combine our beam splitter with on-demand differential phase shifters to create a programmable Mach-Zehnder interferometer that is capable of manipulating two-photon interference on the fly.

Our results pave the way towards scalable boson sampling, linear optical quantum computing in the microwave domain, and quantum algorithms between long-lived bosonic memories.

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Issue

Vol. 8, Iss. 2 — April - June 2018

Subject Areas

Quantum Physics

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Images

Figure 1
cQED system. (a) The effective circuit of the cQED system containing two high- $Q$ harmonic oscillators (orange, blue) bridged by a transmon (green), as well as an additional transmon mode (pink) that only capacitively couples to Alice. A similar ancillary transmon (purple) can also be used, but it is not necessary for this experiment. The resonance frequency of Alice and Bob are detuned from each other by $\sim 1 GHz$ to minimize undesired cross talk. (b) Four-wave mixing process through the Josephson junction of qC that enables the bilinear coupling between Alice and Bob when $ω_{2} - ω_{1} = ω_{b} - ω_{a}$ .
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Figure 2
Calibration of bilinear coupling. (a) General measurement protocol. After preparing the cavities in the desired initial state, we apply the drives for a variable amount of time before measuring the final joint memory state using a photon-number selective $π$ pulse on qC. (b) Measured $P_{10}$ (orange circles) with the engineered interaction at $| ξ_{1} | | ξ_{2} | \approx 0.12$ . Data are normalized by a constant scaling factor to calibrate out the state preparation and measurement errors [23]. Solid line shows fit to the functional form $P_{10} \propto e^{t / τ_{1}} [1 + e^{t / τ_{ϕ}} \sin (2 π t f)]$ . Dashed lines are the intrinsic decays from $| 1 ⟩_{A}$ (gray) and relaxation of $| e ⟩$ (green) of qC. (c) Measured coupling strength $g / 2 π$ (green circles) as a function of the drive strength $| ξ_{1} | | ξ_{2} |$ . Data are consistent with the predicted behavior (black line) based on the fourth order cosine expansion, but deviate at higher drive powers. Measured excited state population of qC (red triangles), after a single BS operation. (d) Measured infidelity of a BS as defined by $τ_{BS} / T_{BS}$ at different drive powers with (black squares) and without (gray crosses) postselecting on qC remaining in its ground state after the operation.
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Figure 3
HOM interference between Alice and Bob. (a) Data show the joint population as the initial state $| 1, 1 ⟩_{AB}$ evolves under ${\hat{U}}_{θ}$ . We observe out-of-phase oscillations between $P_{11}$ and an equal superposition of $| 0, 2 ⟩_{AB}$ and $| 2, 0 ⟩_{AB}$ . (b),(c) 1D cuts to show the behavior of $P_{11}$ (brown) and $P_{02} + P_{20}$ (magenta) up to $\sim 15 μ s$ (red dashed line). A simulation of two indistinguishable photons is shown in solid lines and that of two distinguishable photons is shown in dashed gray lines.
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Figure 4
Measurement of quantum state overlap. (a) When two identical bosonic systems interfere at a $50 ∶ 50$ BS, only even photon-number outcomes are allowed due to the full destructive interference of the odd distributions. This allows us to infer the state overlap $Tr (ρ_{A} ρ_{B})$ from photon-number parity measurement of one of the output ports. (b) The experimental protocol for implementing the overlap measurement between Alice and Bob. (c) Measurement of overlap between $| ψ ⟩_{A} = e^{i ϕ_{A}} | α ⟩$ and $| ψ ⟩_{B} = e^{i ϕ_{B}} | α ⟩$ as a function of the relative displacement angle $(ϕ_{A} - ϕ_{B})$ and amplitude $α$ . Maximum overlap for each displacement is measured when $ϕ_{B} = ϕ_{A}$ (mod $2 π$ ). (d) 1D cut at displacement of $| α |^{2} \approx 2$ . Data are shown in brown circles, which shows good agreement with the overlap determined by full Wigner tomography of each mode, shown in solid gray line. The dashed gray line indicates the predicated peak contrast after taking into account self-Kerr and the decoherence of the cavities.
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Figure 5
Cascaded Mach-Zehnder interferometers composed of BS, DPS, and photon counters. (a) Conceptual implementation of programmable cascaded Mach-Zehnder (MZ) interferometers between two detuned modes. We can measure the state of the system after each operation and implement DPS on demand. (b) Evolution of $| 1, 1 ⟩_{AB}$ in cascaded microwave MZ interferometers, measured by sweeping the frequency of a photon-number selective $π$ pulse on qC while varying the duration of the drive tones. After the first BS, a coherent superposition of $| 0, 2 ⟩_{AB}$ and $| 2, 0 ⟩_{AB}$ ( $| Ψ ⟩$ ) is created. Subsequently, we impart a differential phase $ϕ = π$ , which leaves the system in $| Φ ⟩$ and causes $| 1, 1 ⟩_{AB}$ to destructively interfere through the subsequent BSs. We then introduce another differential phase $π$ such that the system is brought back to the original superposition $| Ψ ⟩$ , which refocuses to $| 1, 1 ⟩_{AB}$ at the subsequent BS, as in standard HOM interference.
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