Dissipative Quantum Research Articles

A short trajectory is all you need: A transformer-based model for long-time dissipative quantum dynamics.

In this Communication, we demonstrate that a deep artificial neural network based on a transformer architecture with self-attention layers can predict the long-time population dynamics of a quantum system coupled to a dissipative environment provided that the short-time population dynamics of the system is known. The transformer neural network model developed in this work predicts the long-time dynamics of spin-boson model efficiently and very accurately across different regimes, from weak system-bath coupling to strong coupling non-Markovian regimes. Our model is more accurate than classical forecasting models, such as recurrent neural networks, and is comparable to the state-of-the-art models for simulating the dynamics of quantum dissipative systems based on kernel ridge regression.

Ultrastrong coupling limit to quantum mean force Gibbs state for anharmonic environment.

The equilibrium state of a quantum system can deviate from the Gibbs state if the system-environment (SE) coupling is not weak. An analytical expression for this mean force Gibbs state (MFGS) is known in the ultrastrong coupling (USC) regime for the Caldeira-Leggett (CL) model that assumes a harmonic environment. Here, we derive analytical expressions for the MFGS in the USC regime for more general SEmodels. For all the generalized models considered here, we find the USC state to be diagonal in the basis set by the SEinteraction, just like in the CL case. While for the generic model considered, the corresponding USC-MFGS is found to alter from the CL result, we do identify a class of models more general than the CL model for which the CL-USC result remains unchanged. We also provide numerical verification for our results. These results provide key tools for the study of strong coupling quantum thermodynamics and several quantum chemistry and biology problems under more realistic SEmodels, going beyond the CL model.

Quantum measurement encoding for quantum metrology

Preserving the precision of the parameter of interest in the presence of environmental decoherence is an important yet challenging task in dissipative quantum sensing. In this work, we study quantum metrology when the decoherence effect is unraveled by a set of quantum measurements, dubbed quantum measurement encoding. In our case, the estimation parameter is encoded into a quantum state through a quantum measurement, unlike the parameter encoding through a unitary channel in the decoherence-free case or trace-preserving quantum channels in the case of decoherence. We identify conditions for a precision-preserving measurement encoding. These conditions can be employed to transfer metrological information from one subsystem to another through quantum measurements. Furthermore, postselected non-Hermitian sensing can also be viewed as quantum sensing with measurement encoding. When the precision-preserving conditions are violated in non-Hermitian sensing, we derive a universal formula for the loss of precision. Published by the American Physical Society 2024

Optimization of Ultrafast Singlet Fission in One-Dimensional Rings Towards Unit Efficiency

Singlet fission (SF) is an electronic transition that in the last decade has been under the spotlight for its applications in optoelectronics, from photovoltaics to spintronics. Despite considerable experimental and theoretical advancements, optimizing SF in materials like multichromophoric systems and molecular crystals remains a challenge, due to the complexity of its analysis beyond perturbative methods. Here, we tackle the case of one-dimensional rings, aiming to promote singlet fission and prevent its backreaction. We study ultrafast SF nonperturbatively, by numerically solving a spin-boson model, via exact propagation and tensor network methods. By optimizing over a parameter space relevant to organic molecular materials, we identify two classes of solutions that can take SF efficiency beyond 85% in the nondissipative (coherent) regime, and to 99% when exciton-phonon interactions can be tuned. After discussing the experimental feasibility of the optimized solutions, we conclude by proposing that this approach can be extended to a wider class of optoelectronic optimization problems. Published by the American Physical Society 2024

Dynamics of the nonequilibrium spin-boson model: A benchmark of master equations and their validity

Dynamics of the nonequilibrium spin-boson model: A benchmark of master equations and their validity

Suppression of quantum dissipation: a cooperative effect of quantum squeezing and quantum measurement.

The ability to isolate a quantum system from its environment is of fundamental interest and importance in optical quantum science and technology. Here we propose an experimentally feasible scheme for beating environment-induced dissipation in an open two-level system coupled to a parametrically driven cavity. The mechanism relies on a novel, to the best of our knowledge, cooperation between light-matter coupling enhancement and frequent measurements. We demonstrate that, in the presence of the cooperation, the system dynamics can be completely dominated by the effective system-cavity interaction, and the dissipative effects from the system-environment coupling can be surprisingly ignored. This work provides a generic method of dissipation suppression in a variety of quantum mechanical platforms, including natural atoms and superconducting circuits.

Capturing Long-Range Memory Structures with Tree-Geometry Process Tensors

We introduce a class of quantum non-Markovian processes—dubbed process trees—that exhibit polynomially decaying temporal correlations and memory distributed across timescales. This class of processes is described by a tensor network with treelike geometry whose component tensors are (1) causality-preserving maps (superprocesses) and (2) locality-preserving temporal change-of-scale transformations. We show that the long-range correlations in this class of processes tends to originate almost entirely from memory effects and can accommodate genuinely quantum power-law correlations in time. Importantly, this class allows efficient computation of multitime correlation functions. To showcase the potential utility of this model-agnostic class for numerical simulation of physical models, we show how it can efficiently approximate the strong memory dynamics of the paradigmatic spin-boson model, in terms of arbitrary multitime features. In contrast to an equivalently costly matrix-product-operator representation, the ansatz produces a fiducial characterization of the relevant physics. Finally, leveraging 2D tensor-network renormalization-group methods, we detail an algorithm for deriving a process tree from an underlying Hamiltonian via the Feynmann-Vernon influence functional. Our work lays the foundation for the development of more efficient numerical techniques in the field of strongly interacting open quantum systems, as well as the theoretical development of a temporal renormalization-group scheme. Published by the American Physical Society 2024

Interaction-induced dissipative quantum phase transition in a head-to-tail atomic Josephson junction

Interaction-induced dissipative quantum phase transition in a head-to-tail atomic Josephson junction

Lyapunov exponent as a signature of dissipative many-body quantum chaos

A distinct feature of Hermitian quantum chaotic dynamics is the exponential increase of certain out-of-time-order correlation (OTOC) functions around the Ehrenfest time with a rate given by a Lyapunov exponent. Physically, the OTOCs describe the growth of quantum uncertainty that crucially depends on the nature of the quantum motion. Here, we employ the OTOC in order to provide a precise definition of dissipative quantum chaos. For this purpose, we compute analytically the Lyapunov exponent for the vectorized formulation of the large-q limit of a q-body Sachdev-Ye-Kitaev model coupled to a Markovian bath. These analytic results are confirmed by an explicit numerical calculation of the Lyapunov exponent for several values of q≥4 based on the solutions of the Schwinger-Dyson and Bethe-Salpeter equations. We show that the Lyapunov exponent decreases monotonically as the coupling to the bath increases and eventually becomes negative at a critical value of the coupling signaling a transition to a dynamics which is no longer quantum chaotic. Therefore, a positive Lyapunov exponent is a defining feature of dissipative many-body quantum chaos. The observation of the breaking of the exponential growth for sufficiently strong coupling suggests that dissipative quantum chaos may require in certain cases a sufficiently weak coupling to the environment. Published by the American Physical Society 2024

Capturing non-Markovian polaron dressing with the master equation formalism.

Understanding the dynamics of open quantum systems in strong coupling and non-Markovian regimes remains a formidable theoretical challenge. One popular and well-established method of approximation in these circumstances is provided by the polaron master equation (PME). In this work, we re-evaluate and extend the validity of the PME to capture the impact of non-Markovian polaron dressing, induced by non-equilibrium open system dynamics. By comparing with numerically exact techniques, we confirm that while the standard PME successfully predicts the dynamics of system observables that commute with the polaron transformation (e.g., populations in the Pauli z-basis), it can struggle to fully capture those that do not (e.g., coherences). This limitation stems from the mixing of system and environment degrees of freedom inherent to the polaron transformation, which affects the accuracy of calculated expectation values within the polaron frame. Employing the Nakajima-Zwanzig projection operator formalism, we introduce correction terms that provide an accurate description of observables that do not commute with the transformation. We demonstrate the significance of the correction terms in two cases, the canonical spin-boson model and a dissipative time-dependent Landau-Zener protocol, where they are shown to impact the system dynamics on both short and long timescales.

Microscopic analysis of relaxation behavior in nonlinear optical conductivity of graphene

We produce a general formalism to study the interband dynamical optical conductivity in the nonlinear regime of graphene in the presence of a quantum bath comprising phonons and electrons. When a quantum solid of graphene is subjected to an intense electric field in the optical frequency range, the observation of a nonlinear response is facilitated by formulating a quantum master equation of the density operator associated with the Hamiltonian encapsulated in a spin-boson model of dissipative quantum statistical mechanics. Our results reveal the nonlinear steady-state regime’s population inversion and decoherence. The present method enables us to investigate further the nonlinear interband optical conductivity of pristine and gapped graphene characterized by a single dimensionless parameter at finite temperatures. Different bath spectra’ effects on phonons and electrons are examined in detail. The temperature dependence of conductivity reveals that changing temperature can enable us to make a transition from the linear to the nonlinear regime for fixed optical field parameters. Interestingly, a fascinating switching-like behavior is observed for the low-temperature optical conductivity of the gapped graphene while we vary the energy gap as well as the frequency of the externally applied field. Although our general formulation can address a variety of nonequilibrium responses of the two-band system, it also facilitates a connection with the phenomenological modeling of nonlinear optical conductivity.

Exploiting automatic differentiation for quantum optimal control of driven dissipative two-level systems

In principle one can use Pontryagin's minimum principle to treat an optimal control problem and derive the gradient for the cost functional. However, for the driven spin-boson model studied here, the response of the system to the variation of the control is determined by the master equation and the equation of motion for the propagator of the coherent system dynamics. As a result, the application of Pontryagin's minimum principle is less straightforward. An alternative to this approach is the technique of automatic differentiation which in principle amounts to doing calculus on the fully discretized form of the optimal control problem. Automatic differentiation tools can be viewed as black boxes taking as input a program computing the cost functional and giving as output another program computing its gradient. First we derive for the polaron transformed Hamiltonian a Born-Markov master equation using the Bloch-Redfield formalism. By combining the latter with automatic differentiation we are able to implement Z-gate and coherent destruction of tunnelling with high fidelity. Optimization of a dissipative quantum gate poses a more complex numerical problem, since it should occur independent of the input state. To overcome this difficulty, we apply optimal control to the concept of resolvent of the master equation which is the generalisation of quantum unitary evolution operator in the case of dissipative dynamics.

Interference effects in nonequilibrium quantum transport with long-range interactions

Abstract We investigate how long-range power-law hopping interaction, ∼ 1/r a , affects the characteristics of dissipative quantum transport in a nonequilibrium setting. The model under consideration is a noninteracting bosonic chain subject to thermal baths of differing temperature at its boundaries and dephasing noise which is applied uniformly to all the sites. It is shown that the steady-state current may vary nonmonotonically and has a peak for a finite a depending on the position of the cold bath. This site-specific behaviour stems back to the interference effect caused by the parity of the total sites N and the baths positions. The fractional nature of the system, along with the interplay between coherent and incoherent transport, will affect the steady state current that characterizes the transport.

Electrostatically Interacting Wannier Qubits in Curved Space

A derivation of a tight-binding model from Schrödinger formalism for various topologies of position-based semiconductor qubits is presented in the case of static and time-dependent electric fields. The simplistic tight-binding model enables the description of single-electron devices at a large integration scale. The case of two electrostatically Wannier qubits (also known as position-based qubits) in a Schrödinger model is presented with omission of spin degrees of freedom. The concept of programmable quantum matter can be implemented in the chain of coupled semiconductor quantum dots. Highly integrated and developed cryogenic CMOS nanostructures can be mapped to coupled quantum dots, the connectivity of which can be controlled by a voltage applied across the transistor gates as well as using an external magnetic field. Using the anti-correlation principle arising from the Coulomb repulsion interaction between electrons, one can implement classical and quantum inverters (Classical/Quantum Swap Gate) and many other logical gates. The anti-correlation will be weakened due to the fact that the quantumness of the physical process brings about the coexistence of correlation and anti-correlation at the same time. One of the central results presented in this work relies on the appearance of dissipation-like processes and effective potential renormalization building effective barriers in both semiconductors and in superconductors between not bended nanowire regions both in classical and in quantum regimes. The presence of non-straight wire regions is also expressed by the geometrical dissipative quantum Aharonov–Bohm effect in superconductors/semiconductors when one obtains a complex value vector potential-like field. The existence of a Coulomb interaction provides a base for the physical description of an electrostatic Q-Swap gate with any topology using open-loop nanowires, with programmable functionality. We observe strong localization of the wavepacket due to nanowire bending. Therefore, it is not always necessary to build a barrier between two nanowires to obtain two quantum dot systems. On the other hand, the results can be mapped to the problem of an electron in curved space, so they can be expressed with a programmable position-dependent metric embedded in Schrödinger’s equation. The semiconductor quantum dot system is capable of mimicking curved space, providing a bridge between fundamental and applied science in the implementation of single-electron devices.

Mpsqd: A matrix product state based Python package to simulate closed and open system quantum dynamics.

We introduce a Python package based on matrix product states (MPS) to simulate both the time-dependent Schrödinger equation (TDSE) and the hierarchical equations of motion (HEOM). The wave function in the TDSE or the reduced density operator/auxiliary density operators in the HEOM are represented using MPS. A matrix product operator (MPO) is then constructed to represent the Hamiltonian in the TDSE or the generalized Liouvillian in the HEOM. The fourth-order Runge-Kutta method and the time-dependent variational principle are used to propagate the MPS. Several examples, including the nonadiabatic interconversion dynamics of the pyrazine molecule, excitation energy transfer dynamics in molecular aggregates and photosynthetic light-harvesting complexes, the spin-boson model, a laser driven two-state model, the Holstein model, and charge transport in the Anderson impurity model, are presented to demonstrate the capability of the package.

Environment-mediated long-ranged correlations in many-body system

Quantum states in complex aggregates are unavoidably affected by environmental effects, which typically cannot be accurately modeled by simple Markovian processes. As system sizes scale up, nonperturbative simulation becomes thus unavoidable, but they are extremely challenging due to the intimate interplay of intrinsic many-body interaction and time-retarded feedback from environmental degrees of freedom. In this work, we utilize the recently developed quantum dissipation with minimally extended state space approach to address reservoir induced long-ranged temporal correlations in finite size Ising-type spin chains. For thermal reservoirs with ohmic and subohmic spectral density, we simulate the quantum time evolution from finite to zero temperature. The competition between thermal fluctuations, quantum fluctuations, and anti-/ferromagnetic interactions reveals a rich pattern of dynamical phases, including dissipative induced phase transitions and spatiotemporal correlations.

Kinetics in the Two-Level System with Strong Time-De-pendent Coupling of Its States to the Phonon Bath: Spin-Boson Description

Using the methods of nonequilibrium statistical mechanics, the master equation for the density matrix of an open dissipative quantum system is obtained under conditions, when the coupling between the electronic states of the system and the nuclear displacements in it is controlled by the alternating field. A time-dependent polaron transformation is proposed, which made it possible to solve kinetic equations using an expansion in a parameter characterizing transitions between “phonon-dressed” electronic states of the system. As an example, a mechanism is shown that can control the kinetics in a two-level system by applying a periodic force field to electron-phonon coupling.

Emergence of subharmonics in a microwave driven dissipative Rydberg gas

Quantum many-body systems near phase transitions respond collectively to externally applied perturbations. We explore this phenomenon in a laser-driven dissipative Rydberg gas that is tuned to a bistable regime. Here two metastable phases coexist, which feature a low and high density of Rydberg atoms, respectively. The ensuing collective dynamics, which we monitor , is characterized by stochastic collective jumps between these two macroscopically distinct many-body phases. We show that the statistics of these jumps can be controlled using a dual-tone microwave field. In particular, we find that the distribution of jump times develops peaks corresponding to subharmonics of the relative microwave detuning. Our study demonstrates the control of collective statistical properties of dissipative quantum many-body systems without the necessity of fine-tuning or of ultracold temperatures. Such robust many-body phenomena may find technological applications in sensing. Published by the American Physical Society 2024

Tensor-network-based variational Monte Carlo approach to the non-equilibrium steady state of open quantum systems

We introduce a novel method of efficiently simulating the non-equilibrium steady state of large many-body open quantum systems with highly non-local interactions, based on a variational Monte Carlo optimization of a matrix product operator ansatz. Our approach outperforms and offers several advantages over comparable algorithms, such as an improved scaling of the computational cost with respect to the bond dimension for periodic systems. We showcase the versatility of our approach by studying the phase diagrams and correlation functions of the dissipative quantum Ising model with collective dephasing and long-ranged power law interactions for spin chains of up to N=100 spins.

Correlation functions from tensor network influence functionals: The case of the spin-boson model.

We investigate the application of matrix product state (MPS) representations of the influence functionals (IFs) for the calculation of real-time equilibrium correlation functions in open quantum systems. Focusing specifically on the unbiased spin-boson model, we explore the use of IF-MPSs for complex time propagation, as well as IF-MPSs for constructing correlation functions in the steady state. We examine three different IF approaches: one based on the Kadanoff-Baym contour targeting correlation functions at all times, one based on a complex contour targeting the correlation function at a single time, and a steady state formulation, which avoids imaginary or complex times, while providing access to correlation functions at all times. We show that within the IF language, the steady state formulation provides a powerful approach to evaluate equilibrium correlation functions.