We theoretically analyze measurements of the transient field leaving a cavity as a tool for studying non-Markovian dynamics in cavity quantum electrodynamics (QED).Combined with a dynamical decoupling pulse sequence, transient spectroscopy can be used to recover spectral features that may be obscured in the stationary cavity transmission spectrum due to inhomogeneous broadening.The formalism introduced here can be leveraged to perform in situ noise spectroscopy, revealing a robust signature of quantum noise arising from noncommuting observables, a purely quantum effect.
We theoretically analyze measurements of the transient field leaving a cavity as a tool for studying non-Markovian dynamics in cavity quantum electrodynamics (QED).Combined with a dynamical decoupling pulse sequence, transient spectroscopy can be used to recover spectral features that may be obscured in the stationary cavity transmission spectrum due to inhomogeneous broadening.The formalism introduced here can be leveraged to perform in situ noise spectroscopy, revealing a robust signature of quantum noise arising from noncommuting observables, a purely quantum effect.
This thesis contains a collection of articles exploring various aspects of quantum information processing with cavity quantum electrodynamics (QED), starting with qubit noise spectroscopy and building towards the longer-term goal of modular quantum-computing architectures equipped with protocols for controlling and correcting the states of distantly separated qubits. The first chapter presents a self-contained introduction to the field of cavity QED. Following this introductory material, we show in Chapter 2 how measurements of the field emitted by a cavity can be leveraged for in-situ qubit noise spectroscopy in the presence of significant inhomogeneous broadening. We also identify a signature of genuinely quantum noise in the cavity output field originating from the non-commutation of bath operators acting on the qubit. In Chapter 3, we present a novel quantum-optical effect whereby a suitable modulation of a longitudinal cavity-qubit coupling can be used to entangle the state of a qubit with the path taken by a multiphoton wavepacket. Entanglement between a qubit and a which-path degree-of-freedom can in turn be used to generate entanglement between distant stationary qubits. As shown in Chapter 4, qubit-which-path entanglement can also be exploited for maximally sensitive estimation of a phase in a Mach-Zehnder interferometry setup, i.e., sensing at the quantum Cramér-Rao bound. In Chapter 5, we discuss strategies for realizing stabilizer measurements using qubit-conditioned phase shifts applied to propagating pulses of radiation. We find that in the context of a subsystem surface code, photon loss during such stabilizer measurements would not introduce any horizontal hook errors on the code qubits. In the sixth and final chapter, we give protocols for performing entangling gates between distant stationary qubits using Fock- or time-bin encoded photons.
Based on the experiments [S. Putz et al., Nat. Phys. 10, 720 (2014); Nat. Photonics 11, 36 (2017)] on the hybrid quantum system of a superconducting microwave cavity coupled strongly to an inhomogeneous broadening spin ensemble, we use the exact master equation theory to investigate its non-Markovian decoherence dynamics under external driving fields. In the experiments, the spin ensemble is made of negatively charged nitrogen-vacancy defects in diamond. The exact master equation theory generalizes the fluctuation-dissipation relation and depicts in details the transient non-Markovian decoherence, in which the dissipation (relaxation) and fluctuations (noise or dephasing) dynamics is well described and the non-Markovian memory effect can be well characterized. We study the physical picture of the transient non-Markovian decoherence dynamics and explore how the non-Markovian decoherence induced by the inhomogeneous broadening of the spin ensemble is suppressed in the strong-coupling regime. We also show how the spectral hole burning generates localized bound states for the further decoherence suppression. Furthermore, we investigate the two-time correlations to show the relationships between quantum fluctuations and quantum memory.
Qubit noise spectroscopy is an important tool for the experimental investigation of open quantum systems. However, conventional techniques for noise spectroscopy are time-consuming, because they require measurements of the noise spectral density at many different frequencies. Here we describe an alternative approach to noise spectroscopy, which requires fewer resources, and relies on direct measurement of arbitrary linear functionals of the noise spectral density. This method uses random pulse sequences with carefully controlled correlations, which are chosen using algorithms for phase retrieval. These measurements allow us to reconstruct sparse noise spectra via compressed sensing. Our simulations of the performance of the random pulse sequences on a realistic physical system, self-assembled quantum dots, reveal a speedup of an order of magnitude in extracting the noise spectrum, compared to conventional dynamical decoupling approaches.
I present a theory of environmental noise spectroscopy via dynamical decoupling of a qubit at an optimal working point. Considering a sequence of n pulses and pure dephasing due to quadratic coupling to Gaussian distributed noise $\ensuremath{\xi}(t)$, I use the linked-cluster (cumulant) expansion to calculate the coherence decay. Solutions allowing for reconstruction of spectral density of noise are given. For noise with correlation time shorter than the time scale on which coherence decays, the noise filtered by the dynamical decoupling procedure can be treated as effectively Gaussian at large n, and well-established methods of noise spectroscopy can be used to reconstruct the spectrum of ${\ensuremath{\xi}}^{2}(t)$ noise. On the other hand, for noise of dominant low-frequency character $(1/{f}^{\ensuremath{\beta}}$ noise with $\ensuremath{\beta}>1)$, an infinite-order resummation of the cumulant expansion is necessary, and it leads to an analytical formula for coherence decay having a power-law tail at long times. In this case, the coherence at time t depends both on spectral density of $\ensuremath{\xi}(t)$ noise at $\ensuremath{\omega}=n\ensuremath{\pi}/t$, and on the effective low-frequency cutoff of the noise spectrum, which is typically given by the inverse of the data acquisition time. Simulations of decoherence due to purely transverse noise show that the analytical formulas derived in this paper apply in this often encountered case of an optimal working point, provided that the number of pulses is not very large, and that the longitudinal qubit splitting is much larger than the transverse noise amplitude.
Memory or time-non-local effects in open quantum dynamics pose theoretical as well as practical challenges in the understanding and control of noisy quantum systems. While there has been a comprehensive and concerted effort towards developing diagnostics for non-Markovian dynamics, all existing measures rely on time-domain measurements which are typically slow and expensive as they require averaging several runs to resolve small transient features on a broad background, and scale unfavorably with system size and complexity. In this work, we propose a spectroscopic measure of non-Markovianity which can detect persistent non-Markovianity in the system steady state. In addition to being experimentally viable, the proposed measure has a direct information theoretic interpretation: a large value indicates the information loss per unit bandwidth of making the Markov approximation. In the same vein, we derive a frequency-domain quantum master equation (FD-QME) that goes beyond the standard Born-Redfield description and retains the full memory of the state of the reduced system. Using the FD-QME and the proposed measure, we are able to reliably diagnose and quantify non-Markovianity in several system-environment settings including those with environmental correlations and retardation effects.
Quantum state transfer into a memory, state shuttling over long distances via a quantum bus, and high-fidelity readout are important tasks for quantum technology. Realizing these tasks is challenging in the presence of realistic couplings to an environment. Here, we introduce and assess protocols that can be used in cavity quantum electrodynamics to perform high-fidelity quantum state transfer and fast quantum nondemolition qubit readout through Hamiltonian engineering. We show that high-fidelity state transfer between a cavity and a single qubit can be performed, even in the limit of strong dephasing due to inhomogeneous broadening. We generalize this result to state transfer between a cavity and a logical qubit encoded in a collective mode of a large ensemble of N physical qubits. Under a decoupling sequence, we show that inhomogeneity in the ensemble couples two collective bright states to only two other collective modes, leaving the remaining single-excitation states dark. Moreover, we show that large signal-to-noise and high single-shot fidelity can be achieved in a cavity-based qubit readout, even in the weak-coupling limit. These ideas may be important for novel systems coupling single spins to a microwave cavity.