In waveguide quantum electrodynamics (QED) systems, a giant cavity can be engineered to interact with quantum fields by multiple distant coupling points so that its non-Markovian dynamics are quite different from traditional quantum optical cavity systems. Towards feedback control this system, this paper designs an optimal filter for the giant cavity systems to estimate its state evolution under continuous quantum measurements. Firstly, the Langevin equation in the Heisenberg picture are derived, which is a linear continuous-time system with both states and inputs delays resulting from the unconventional distant couplings. Compared to existing modeling approaches, this formulation effectively preserves the nonlocal coupling and multiple delay dynamic characteristics inherent in the original system. In particular, the presence of coupling and propagation delays leads to noncommutativity among the system operators at different times, which prevents the direct application of existing quantum filtering methods. To address this issue, an optimal filter is designed, in which the delayed-state covariance matrices are computed. By iteratively evaluating the delayed-state covariance over successive time intervals, the resulting optimal filter can be implemented in an interval-wise backward recursion algorithm. Finally, numerical simulations are conducted to evaluate the tracking performance of the proposed optimal filter for the giant cavity. By comparing between the evolutions of Wigner functions of coherent and cat states and the filter, the effectiveness of the optimal filter is validated.
In waveguide quantum electrodynamics (QED) systems, a giant cavity can be engineered to interact with quantum fields by multiple distant coupling points so that its non-Markovian dynamics are quite different from traditional quantum optical cavity systems. Towards feedback control this system, this paper designs an optimal filter for the giant cavity systems to estimate its state evolution under continuous quantum measurements. Firstly, the Langevin equation in the Heisenberg picture are derived, which is a linear continuous-time system with both states and inputs delays resulting from the unconventional distant couplings. Compared to existing modeling approaches, this formulation effectively preserves the nonlocal coupling and multiple delay dynamic characteristics inherent in the original system. In particular, the presence of coupling and propagation delays leads to noncommutativity among the system operators at different times, which prevents the direct application of existing quantum filtering methods. To address this issue, an optimal filter is designed, in which the delayed-state covariance matrices are computed. By iteratively evaluating the delayed-state covariance over successive time intervals, the resulting optimal filter can be implemented in an interval-wise backward recursion algorithm. Finally, numerical simulations are conducted to evaluate the tracking performance of the proposed optimal filter for the giant cavity. By comparing between the evolutions of Wigner functions of coherent and cat states and the filter, the effectiveness of the optimal filter is validated.
In this paper, we present an H∞filter for a giant cavity system which couples to a single-mode waveguide at two spatially separated points. The dynamics of the cavity is described by a time-delay Langevin equation in the Heisenberg picture whose time-delay term results from the non-local interactions to a waveguide. The input-output relation with a time-delay feature is also derived. In addition, we design an H∞filter for estimating the evolution of the mode in the cavity using a quadrature representation state-space representation and Linear Matrix Inequality (LMI) approach. Finally, the efficacy of our method is numerically demonstrated in an example.
We study the generation of quantum entanglement between two giant atoms coupled to a common one-dimensional waveguide. Here each giant atom interacts with the waveguide at two separate coupling points. Within the Wigner-Weisskopf framework for single coupling points, we obtain the time-delayed quantum master equations governing the evolution of the two giant atoms for three different coupling configurations: separated, braided, and nested couplings. For each coupling configuration, we consider both the Markovian and non-Markovian entanglement dynamics of the giant atoms, which are initially in two different separable states: single- and double-excitation states. Our results show that the generated entanglement depends on the phase shift, time delay, atomic initial state, and the coupling configuration. For the single-excitation initial state, there exists the steady-state entanglement for each coupling in both the Markovian and non-Markovian regimes due to the appearance of the dark state. For the double-excitation initial state, we observe entanglement sudden birth via adjusting the phase shift in both regimes. In particular, the maximally achievable entanglement for the nested coupling is about one order of magnitude larger than those of separate and braided couplings. We also find that the maximal entanglement for these three coupling configurations can be enhanced in the case of small time delays. This work can be utilized for the generation and control of entanglement in quantum networks based on giant-atom waveguide-QED systems, which have wide potential applications in quantum information processing.
We study the Markovian and non-Markovian dynamics in a giant atom system which couples to a coupled resonator waveguide (CRW) via two distant sites. Under certain conditions, we find that the giant atom population can exhibit an oscillating behavior and the photon can be trapped in the giant atom regime. These phenomena are induced by the interference effect among the bound states both in and outside the continuum, which is peculiar for two-site atom-CRW coupling. As an application of the photon trapping, we theoretically propose a magic cavity model where the giant atom serves as either a perfect or leaky cavity, depending on the distance between the coupling sites. The controllability of the magic cavity from a perfect to a leaky one cannot be realized in the traditional cavity or circuit QED setup. The predicted effects can be probed in state-of-the-art waveguide QED experiments and provide a striking example of how the different kinds of bound states modify the dynamics of a quantum open system in a structured environment.
The emergence of integrated (or solid state) photonic systems, including quantum dots, waveguides, and cavities, has provided a base to harness quantum optic phenomena for use in current and future quantum technologies. These systems also provide opportunities for exploring fundamentally new regimes in quantum optics. In order to fully realize the potential of these systems, many figures of merit need to be improved, for example by increasing the stability and coherent lifetimes of these systems. Following the notable improvements using measurement-based feedback, time-delayed coherent optical feedback has been proposed as one such method of stabilizing and improving these systems. Furthermore, modelling coherent feedback itself presents an interesting fundamental problem due to its non-Markovian nature. In this thesis, we use quantum trajectory (QT) theory to derive two models for simulating cavity quantum electrodynamic (cavity-QED) systems with time-delayed coherent feedback. First, an explanation of QT theory is given and the related time discretized waveguide (TDW) model is derived. Next we present a model for feedback using the frequency modes of the waveguide and results are presented in the ``one photon in the loop" approximation. We demonstrate how the photon lifetime can be improved in typical cavity-QED with coherent feedback and we explore some nonlinear effects. We then expand the system to allow for two photons in the feedback loop which requires us to use the TDW model. Lastly, this new approach is used to model two two-level systems coupled via a waveguide and connected to a feedback loop. These findings have implications on improving quantum optic systems by creating a new degree of control, as well as for modelling non-Markovian features in quantum optics.
Recent progress has revealed that quantum systems with multiple position-dependent couplings, e.g., giant atoms, can exhibit some unconventional phenomena, such as non-exponential decay. However, their potential applications are still open questions. In this paper, we propose a giant-cavity-based quantum sensor for the first time, whose performance can be greatly enhanced compared to traditional cavity-based sensors. In our proposal, two cavities are coupled to a dissipative reservoir at multiple points while they couple to a gain reservoir in a single-point way. To detect an unknown parameter entering the sensor, a waveguide is coupled to one of the cavities where detecting fields can pass through for homodyne detection. We find that multiple position-dependent couplings can induce an inherent non-reciprocal coupling between the cavities, which can enhance the performance of sensors. Compared to the results in the work of Lau and Clerk, (Nat Commun, 2018, 9: 4,320), our output noise can remain at the shot noise level, which is about one order of magnitude lower. In addition, the signal-to-noise ratio per photon is also enhanced by about one order of magnitude. These results showed that the multiple-point coupling structure is beneficial to existing quantum devices.
We propose a stochastic Schrödinger equation (SSE) approach to investigate the dynamics of giant atoms coupled to a waveguide, addressing two critical gaps in existing research, namely insufficient exploration on continuous coupling and multiple excitations. A key finding is that continuous coupling, unlike discrete coupling at finite points, breaks the constant phase difference condition, thereby weakening the interference effects in giant atom-waveguide systems. In addition, a key technical advantage of the SSE approach is that auto- and cross-correlation functions can directly reflect the complex photon emission/absorption processes and time-delay effects in giant atom-waveguide systems. Moreover, the SSE approach also naturally handles multiple excitations, without increasing equation complexity as the number of excitations grows. This feature enables the investigation of multi-excitation initial states of the waveguide, such as thermal and squeezed initial states. Overall, our approach provides a powerful tool for studying the dynamics of giant atoms coupled to waveguide, particularly for continuous coupling and multi-excitation systems.