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arXiv:1502.00607 · Physical Review Letters

Heisenberg-Limited Qubit Read-Out with Two-Mode Squeezed Light

Nicolas Didier, Archana Kamal, William D. Oliver, Alexandre Blais, Aashish A. Clerk

Published Aug 27, 2015• 54 citations
arXivHTMLPDF

Abstract

We show how to use two-mode squeezed light to exponentially enhance cavity-based dispersive qubit measurement. Our scheme enables true Heisenberg-limited scaling of the measurement, and crucially, it is not restricted to small dispersive couplings or unrealistically long measurement times. It involves coupling a qubit dispersively to two cavities and making use of a symmetry in the dynamics of joint cavity quadratures (a so-called quantum-mechanics-free subsystem). We discuss the basic scaling of the scheme and its robustness against imperfections, as well as a realistic implementation in circuit quantum electrodynamics.

DOI
10.1103/physrevlett.115.093604

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We show how to use two-mode squeezed light to exponentially enhance cavity-based dispersive qubit measurement. Our scheme enables true Heisenberg-limited scaling of the measurement, and crucially, it is not restricted to small dispersive couplings or unrealistically long measurement times. It involves coupling a qubit dispersively to two cavities and making use of a symmetry in the dynamics of joint cavity quadratures (a so-called quantum-mechanics-free subsystem). We discuss the basic scaling of the scheme and its robustness against imperfections, as well as a realistic implementation in circuit quantum electrodynamics.
Squeezed states of light are a set of nonclassical states in which the quantum fluctuations of one quadrature component are reduced below the standard quantum limit. With less noise than the best stabilised laser sources, squeezed light is a key resource in the field of quantum technologies and has already improved sensing capabilities in areas ranging from gravitational wave detection to biomedical applications. In this work we propose a novel technique for generating squeezed states of a confined light field strongly coupled to a two-level system, or qubit, in the dispersive regime. Utilising the dispersive energy shift caused by the interaction, control of the qubit state produces a time-dependent change in the frequency of the light field. An appropriately timed sequence of sudden frequency changes reduces the quantum noise fluctuations in one quadrature of the field well below the standard quantum limit. The degree of squeezing and the time of generation are directly controlled by the number of frequency shifts applied. Even in the presence of realistic noise and imperfections, our protocol promises to be capable of generating a useful degree of squeezing with present experimental capabilities.
Squeezed light can exponentially increase the signal-to-noise ratio (SNR) of dispersive qubit readout, especially using a combination of injected external squeezing (IES) and intracavity squeezing (ICS). We further investigate whether IES and ICS can also exponentially improve the measurement precision of temperature. In the case of fully thermalized qubits isolated from a thermal bath, the measurement precision of temperature can be improved exponentially when the temperature, the measurement time, or the input photon number approaches 0. In general, thermal fluctuations prevent the action of squeezed light. When multiple qubits maintain interacting with the thermal bath, the Heisenberg scaling can be achieved if the loss rate of the cavity is large and the coupling between the qubit and the optical cavity is weak enough. In the meantime, IES can also further promote the improvement of the measurement precision of the temperature exponentially.
We introduce and analyze a dispersive qubit readout scheme where two-mode squeezing is generated directly in the measurement cavities. The resulting suppression of noise enables fast, high-fidelity readout of naturally weakly coupled qubits, and the possibility to protect strongly coupled qubits from decoherence by weakening their coupling. Unlike other approaches exploiting squeezing, our setup avoids the difficult task of transporting and injecting with high fidelity an externally generated squeezed state. Our setup is also surprisingly robust against unwanted non-QND backaction effects, as interference naturally suppresses Purcell decay: the system acts as its own Purcell filter. Our setup is compatible with the experimental state-of-the-art in circuit QED systems, but the basic idea could also be realized in other systems.
We investigate the quantum measurement physics of a system in which a phase-sensitive parametric amplifier is used to directly measure a qubit to which it is coupled dispersively. By analytic calculation of the signal-to-noise ratio, we show that the amplification properties of the paramp can be exploited to achieve on-chip gain of the qubit readout signal, mitigating the damage done to the measurement rate by circulator added noise and losses in between the readout cavity and any following amplification chain. With a different choice of drive phase, we show that when added noise is not a concern, the squeezing properties of the paramp can be used to enhance the measurement rate relative to a standard dispersive readout by reducing the readout noise without corresponding reduction of qubit signal. We then proceed to calculate the back-action dephasing of the qubit by way of a phase-space technique, and find analytic results valid in the long-time limit while numerically handling the finite-time case. We show how in both operating modes, in the long-time limit, the back-action dephasing of the qubit can be made as small as is allowed by quantum mechanics by using using sufficiently many photons in the measurement, i.e.\@ by using a sufficiently strong coherent measurement drive. Crucially, we find that in the presence of experimentally realistic amounts of added noise, the on-chip gain afforded by such a device can be used to come significantly closer to the quantum limit than is possible with a standard dispersive measurement setup, allowing for efficiencies of ~ 75% under conditions that would yield efficiencies <~ 1 % when applying the usual scheme.
We study theoretically a three-mode optomechanical system where two mechanical oscillators are coupled to a single cavity mode. By using two-tone (i.e., amplitude-modulated) driving of the cavity, it is possible to couple the cavity to a single collective quadrature of the mechanical oscillators. In such a way, a back-action-evading measurement of the collective mechanical quadrature is possible. We discuss how this can allow one to measure both quadratures of a mechanical force beyond the full quantum limit, paying close attention to the role of dissipation and experimental imperfections. We also describe how this scheme allows one to generate steady-state mechanical entanglement; namely, one can conditionally prepare an entangled, two-mode squeezed mechanical state. This entanglement can be verified directly from the measurement record by applying a generalized version of Duan's inequality; we also discuss how feedback can be used to produce unconditional entanglement.
Fault-tolerant quantum information processing with flawed qubits and gates requires highly efficient, quantum nondemolition qubit readout. In superconducting circuits, qubit readout using coherent light with fidelity above 99% has been achieved by using quantum limited parametric amplifiers such as the Josephson parametric converter (JPC). However, further improvement of such measurement faces many challenges, including the vacuum fluctuation of the coherent light that limits measurement fidelity. In this work we demonstrate dispersive qubit readout with a two-mode squeezed light interferometer formed by two JPCs. The first JPC generates two-mode squeezed vacuum at its output, which is coherently recombined by the second JPC after one branch is phase shifted and displaced by its interaction with the qubit-cavity system on that arm of the interferometer. We observe a 31% improvement in the power signal-to-noise ratio (SNR) of projective readout after replacing vacuum fluctuation in the readout cavity with two-mode squeezed vacuum containing on average one photon. This demonstrates a more efficient way of improving SNR than by increasing readout power. Furthermore, we investigate the quantum properties of the two-mode squeezed light in the system through weak measurement. Surprisingly, we find that tuning the interferometer to be less projective increases the measurement efficiency relative to the optimum setting for projective measurement. These enhancements may enable remote entanglement with lower efficiency components in a system with qubits in both arms of the interferometer.