We present a scheme to efficiently simulate nonreciprocal many-body spin models using a non-Markovian open system. Our scheme utilizes a single quantum emitter coupled to a waveguide mode that is fed back to the same emitter after a time delay. With this coherent delayed feedback, an effective nonreciprocal interaction can be engineered, wherein the emitter at earlier times affects itself at later times, creating a scalable spin chain. We show that all the steady-state quantities of such spin models can be accessed through measurement of the emitter and the output field. Furthermore, using classical feedback that resets the emitter, quench dynamics from arbitrary product states can be simulated. We demonstrate striking features of nonreciprocal models, such as the Liouvillian skin effect, anomalous relaxation dynamics, and quasi-long-range order of output photons. Finally, we show that the proposal is amenable to experimental realization and robust to imperfections. Our work establishes a feasible way to scale up a nonreciprocal many-body system, and provides a new route towards generation of exotic states of light.
We present a scheme to efficiently simulate nonreciprocal many-body spin models using a non-Markovian open system. Our scheme utilizes a single quantum emitter coupled to a waveguide mode that is fed back to the same emitter after a time delay. With this coherent delayed feedback, an effective nonreciprocal interaction can be engineered, wherein the emitter at earlier times affects itself at later times, creating a scalable spin chain. We show that all the steady-state quantities of such spin models can be accessed through measurement of the emitter and the output field. Furthermore, using classical feedback that resets the emitter, quench dynamics from arbitrary product states can be simulated. We demonstrate striking features of nonreciprocal models, such as the Liouvillian skin effect, anomalous relaxation dynamics, and quasi-long-range order of output photons. Finally, we show that the proposal is amenable to experimental realization and robust to imperfections. Our work establishes a feasible way to scale up a nonreciprocal many-body system, and provides a new route towards generation of exotic states of light.
ABSTRACT The phenomenon of quantum walks of quasiparticles under nonreciprocal coupling is not only pivotal for investigating a myriad of novel quantum phenomena in nonreciprocal many‐body quantum systems, but also holds promise for the construction of nonreciprocal quantum devices. To date, manipulating the dynamical behavior of quasiparticles in such systems remains a significant challenge. Leveraging the quantum interference effect between coherent and dissipative coupling channels, we propose an effective scheme for realizing nonreciprocal coupling between superconducting qubits, and based on this scheme, we present a one‐dimensional nonreciprocal quantum simulator. Through numerical simulations, we demonstrate that this quantum simulator is capable of precisely manipulating a variety of exotic quantum phenomena, including the non‐Hermitian skin effect, chiral currents, and chiral spin waves. Furthermore, we simulate the propagation dynamics of entangled states under nonreciprocal coupling; the results indicate that nonreciprocity significantly suppresses the propagation of entanglement. Moreover, we provide a phenomenological interpretation of these exotic physical phenomena emerging in the non‐Hermitian regime. The nonreciprocal coupling mechanism and the quantum simulator presented in this work provide a highly coherent, scalable, and controllable platform for the quantum simulation of nonreciprocal many‐body systems, paving the way for the design of nonreciprocal quantum devices.
Time-delayed quantum feedback is a fast and efficient method to control and stabilize few and many-body quantum systems. However, a proper understanding of such systems stays opaque due to the non-Markovian nature of the feedback protocol. Here, we present a method of encoding time-delayed quantum feedback into a chain of nonreciprocally coupled auxiliary oscillators. Our approach serves as a novel method of introducing time-delayed quantum feedback and provides the advantage of large tunability. Importantly, within our approach the original non-Markovian system is embedded into an enlarged Markovian open quantum system, which can be treated efficiently with quantum many-body methods. As an exemplary illustration, we apply our Markovian embedding approach to the paradigmatic case of a driven-dissipative atom in front of a mirror.
The study of open quantum systems forms one of the main problems of modern physics. This thesis aims at contributing to this field, and focuses on the investigation of non-Markovian dynamics of open quantum systems. Here, as a special case, quantum many-body systems provide for a rich field of research. With the ability to control them being of essential importance for the development of quantum technologies, the characterization of their dynamical properties has also drawn a lot of interest lately. One of the main methodological tasks in the study of open quantum systems is to reduce the infinite degrees of freedom of the total system. In order to achieve this, the thesis makes use of the tensor network method matrix product states and combines it with the picture of the quantum stochastic Schrödinger equation. However, when computing the dynamics of many-body systems of system size N, even the reduced system dynamics scale with 2N, making larger system sizes difficult to access. Therefore, especially when computing non-Markovian time-dynamics where the information backflow from the reservoir has to be taken into account, efficiently constructed algorithms are required. This thesis proposes these type of algorithms and demonstrates their application. They enable an access to larger system sizes, thus making it possible to investigate non-equilibrium steady-states of quantum many-body systems in a non-Markovian interaction for system sizes up to N=30. This thesis consists of three parts. The first part provides an introduction to the theory of open quantum systems and to the methodology for modeling them. The second part examines many-body system-reservoir interaction in the non-Markovian regime by investigating the case of fully coherent self-feedback. It uses the one-dimensional Heisenberg spin-1/2 chain as a paradigmatic and recently intensely studied many-body system. It is demonstrated that this gives rise to new conditions for the feedback phase and to highly non-trivial states within the system as well as to the possibility of partially characterizing the system non-invasively and storing excitation within it. Next, a novel approach to the boundary-driven Heisenberg chain is presented, where the chain is exposed to a coherent driving field, thus enabling a comparison to the well-studied incoherently driven model. The third part demonstrates the use of an external pump to control the feedback phase of a Lambda-type three-level system, where the external pump pulse is shown to be a new control parameter. The thesis concludes with the proposition to enhance the indistinguishability of two photons by feedback control.
To continue developing quantum technologies, such as quantum computing, quantum communication and quantum cryptography, we need reliable sources of quantum states of light. These quantum states of light can come in many forms; single photons, entangled pairs, bunched and anti-bunched light, all have uses in current quantum technologies, but for the best performance, this light must maintain its coherence. Time-delayed coherent feedback is a passive feedback method proposed for waveguide quantum electrodynamic systems to improve their performance and unlock new quantum optical phenomena. Additionally, due to its underlying non-Markovian dynamics, feedback is also an interesting theoretical problem to study. In this thesis, we use a quantum trajectory discretized waveguide (QTDW) model to simulate feedback dynamics and investigate its effects in a variety of applications. Originally proposed by Whalen in 2018, we develop the QTDW model beyond its initial implementation to now calculate quantum correlation functions, output spectra, waiting time distributions, and single photon source figures of merit. First, we present an explanation of quantum trajectory theory which is used to model the time dynamics in the QTDW approach, and discuss feedback in the linear regime to highlight the differences between Markovian and non-Markovian dynamics with coherent feedback. We next present nonlinear spectra and multi-photon effects from coherent feedback highlighting how the typical Mollow triplet is dressed by the feedback to create new resonances in the output field. This is followed by a collaborative theory and experiment work which observed our predicted non-Markovian signatures in the nonlinear output spectrum along with new non-Markovian phenomena in the linear regime. We then investigate how pulse-triggered single photon sources can be improved through the inclusion of a time-delayed coherent feedback, presenting the possible improvement to the performance figures of merit. Lastly, the modeling techniques developed for single photon sources with feedback are used to compare the performance of three new off-resonant driving techniques for on-demand single photon sources. These findings show time-delayed coherent feedback is an excellent degree of control to include in future waveguide quantum electrodynamic systems to unlock better performance and new phenomena in the system under investigation.
We study the dynamics of photonic quantum circuits consisting of nodes coupled by quantum channels. We are interested in the regime where the time delay in communication between the nodes is significant. This includes the problem of quantum feedback, where a quantum signal is fed back on a system with a time delay. We develop a matrix product state approach to solve the quantum stochastic Schrödinger equation with time delays, which accounts in an efficient way for the entanglement of nodes with the stream of emitted photons in the waveguide, and thus the non-Markovian character of the dynamics. We illustrate this approach with two paradigmatic quantum optical examples: two coherently driven distant atoms coupled to a photonic waveguide with a time delay, and a driven atom coupled to its own output field with a time delay as an instance of a quantum feedback problem.
This paper presents an efficient algorithm for the time evolution of open quantum many-body systems using matrix-product states (MPS) proposing a convenient structure of the MPS-architecture, which exploits the initial state of system and reservoir. By doing so, numerically expensive re-ordering protocols are circumvented. It is applicable to systems with a Markovian type of interaction, where only the present state of the reservoir needs to be taken into account. Its adaption to a non-Markovian type of interaction between the many-body system and the reservoir is demonstrated, where the information backflow from the reservoir needs to be included in the computation. Also, the derivation of the basis in the quantum stochastic Schrödinger picture is shown. As a paradigmatic model, the Heisenberg spin chain with nearest-neighbor interaction is used. It is demonstrated that the algorithm allows for the access of large systems sizes. As an example for a non-Markovian type of interaction, the generation of highly unusual steady states in the many-body system with coherent feedback control is demonstrated for a chain length of N=30.