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arXiv:1906.00765 · Physical Review A

Dispersive readout of a weakly coupled qubit via the parity-time-symmetric phase transition

Guo-Qiang Zhang, Yi‐Pu Wang, J. Q. You

Published May 28, 2019• 19 citations
arXivHTMLPDF

Abstract

For some cavity-quantum-electrodynamics systems, such as a single-electron spin coupled to a passive cavity, it is challenging to reach the strong-coupling regime. In such a weak-coupling regime, the conventional dispersive readout technique cannot be used to resolve the quantum states of the spin. Here we propose an improved dispersive readout method to measure the quantum states of a weakly coupled qubit by harnessing either one or two auxiliary cavities linearly coupled to the passive cavity containing the qubit. With appropriate parameters in both cases, the system excluding the qubit can exhibit a parity-time-symmetric phase transition at the exceptional point (EP). Because the EP can amplify the perturbation induced by the qubit and the parity-time symmetry can narrow the linewidths of the peaks in the transmission spectrum of the passive cavity, we can measure the quantum states of the weakly coupled qubit via this transmission spectrum. Owing to the weak coupling between the qubit and the passive cavity, the backaction due to the measurement of the qubit can also be reduced in comparison with the conventional dispersive readout technique in the strong-coupling regime.

DOI
10.1103/physreva.99.052341

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For some cavity-quantum-electrodynamics systems, such as a single-electron spin coupled to a passive cavity, it is challenging to reach the strong-coupling regime. In such a weak-coupling regime, the conventional dispersive readout technique cannot be used to resolve the quantum states of the spin. Here we propose an improved dispersive readout method to measure the quantum states of a weakly coupled qubit by harnessing either one or two auxiliary cavities linearly coupled to the passive cavity containing the qubit. With appropriate parameters in both cases, the system excluding the qubit can exhibit a parity-time-symmetric phase transition at the exceptional point (EP). Because the EP can amplify the perturbation induced by the qubit and the parity-time symmetry can narrow the linewidths of the peaks in the transmission spectrum of the passive cavity, we can measure the quantum states of the weakly coupled qubit via this transmission spectrum. Owing to the weak coupling between the qubit and the passive cavity, the backaction due to the measurement of the qubit can also be reduced in comparison with the conventional dispersive readout technique in the strong-coupling regime.
In this paper we study the dispersive readout of a driven three-level atom weakly interacting with a passive cavity that couples to an active cavity. The system excluding the three-level atom exhibits a parity-time (PT\mathcal{P}\mathcal{T}PT) symmetric phase transition at the exceptional point (EP), which originates from the balance between dissipation of the passive cavity and gain of the active cavity. The perturbation to the passive cavity induced by the three-level atom can be amplified near the EP, where the eigenvalues of the effective Hamiltonian have significant differences when the three-level atom is in the excited, metastable, and ground states, respectively. Applying the modified Laplace transformation and input-output theory near the EP, we can realize the dispersive readout of the three-level atom weakly interacting with coupled cavities, which can be characterized through the different distributions of the transmission spectrum of the passive cavity and the ratio of the active cavity excitation number to the input photon number corresponding to the different levels of the three-level atom. Moreover, we generalize the dispersive readout method to the non-Markovian regime, which is in good agreement with that obtained by the Markovian approximation. We find that the non-Markovian effects of the environment backacting on the system dynamics can lead to the enhancement of the dispersive readout for the three-level atom, which is revealed by the excitation backflow generated in the interaction between the passive cavity and environment. The dispersive readout proposed is conducive to understanding the influences of PT\mathcal{P}\mathcal{T}PT symmetry and the non-Markovian effect on dispersive readout, which offers the possibility of an alternative field of possible applications for quantum information and quantum communication.
We propose a quantum state readout mechanism of a weakly coupled qubit in a dispersive regime. The hybrid system consists of a ferromagnetic insulator and a weakly coupled quantum system, e.g., single electron spin, in a microwave cavity. The enhancement of the measurement sensitivity is achieved by exerting torque on the ferromagnetic insulator magnetization, which compensates the damping of the system leading to an exceptional point. The proposed mechanism allows us to measure the qubit state either via the transmission of the cavity or the FMR signal of the magnetic material.
We propose a paradigm of multiplexed dispersive qubit measurement performed while the qubits dephase. A Laplace transformation of the time-dependent cavity response allows to separate contributions from multiple qubits coupled to the same resonator mode, thus allowing for simultaneous single-shot readout. With realistic parameters for silicon spin qubits we find a competitive readout fidelity, while the measurement time compares favorably to conventional dispersive readout. We extend the multiplexed readout method to quantum nondemolition measurements using auxiliary qubits.
We describe a tunable-cavity quantum electrodynamics (QED) architecture with an rf SQUID phase qubit inductively coupled to a single-mode, resonant cavity with a tunable frequency that allows for both microwave readout of tunneling and dispersive measurements of the qubit. Dispersive measurement is well characterized by a three-level model, strongly dependent on qubit anharmonicity, qubit-cavity coupling, and detuning. A tunable-cavity frequency provides a way to strongly vary both the qubit-cavity detuning and coupling strength, which can reduce Purcell losses, cavity-induced dephasing of the qubit, and residual bus coupling for a system with multiple qubits. With our qubit-cavity system, we show that dynamic control over the cavity frequency enables one to avoid Purcell losses during coherent qubit evolutions and optimize state readout during qubit measurements. The maximum qubit decay time ${T}_{1}=1.5\phantom{\rule{0.222222em}{0ex}}\ensuremath{\mu}$s is found to be limited by surface dielectric losses from a design geometry similar to planar transmon qubits.
The conventional method of qubit measurements in circuit QED is employing the dispersive regime of qubit-cavity coupling, which results in an approximated scheme of quantum nondemolition (QND) readout. This scheme becomes problematic in the case of strong coupling and/or strong measurement drive, owing to the so-called Purcell effect. A recent proposal by virtue of longitudinal coupling suggests a new scheme to realize fast, high-fidelity, and ideal QND readout of qubit state. The aim of the present work is twofold: (i) In parallel to what has been done in the past years for the dispersive readout, we carry out the gradual partial-collapse theory for this recent scheme, in terms of both the quantum trajectory equation and quantum Bayesian approaches. The partial-collapse weak measurement theory is useful for such as the measurement-based feedback control and other quantum applications. (ii) In the physical aspect, we construct the joint qubit-plus-cavity entangled state under continuous measurement and present a comprehensive analysis for the quantum efficiency, qubit-state purity, and signal-to-noise ratio in the output currents. The combination of the joint state and the quantum Bayesian rule provides a generalized scheme of cavity reset associated with the longitudinal coupling, which can restore the qubit to a quantum pure state from entanglement with the cavity states, and thus benefits the successive partial-collapse measurements after qubit rotations.
We analyze a two-qubit parity measurement based on dispersive readout in circuit quantum electrodynamics. The back action on the qubits has two qualitatively different contributions. One is an unavoidable dephasing in one of the parity subspaces, arising during the transient time of switching on the measurement. The other part is a stochastic rotation of the phase in the same subspace, which persists during the whole measurement. The latter can be determined from the full measurement record using the method of state estimation. Our main result is that the outcome of this phase determination process is independent of the initial state in the state estimation procedure. The procedure can thus be used in a measurement situation where the initial state is unknown. We discuss how this feedback method can be used to achieve a high-fidelity parity measurement for moderate values of the cavity-qubit coupling strength. Finally, we discuss the robustness of the feedback procedure toward errors in the measurement record.