Session M27: Open Quantum Systems

Live

Ultracold atomic gases provide a clean setting for the study of mesoscopic systems, which are characterized by the importance of fluctations of their constituent particles. However, detection of ultracold atomic gases is typically destructive, precluding repeated measurements on the same sample. In our experiment, we overcome this limitation by utilizing the enhanced light-matter coupling in a high-finesse optical cavity. We use a non-invasive measurement scheme to record real-time traces of the atom number dynamics in a mesoscopic quantum gas undergoing evaporative cooling. Extracting two-time correlation functions from our measurements, we reveal the non-linear dynamics of the evaporating gas. This allows for exploring the intriguing interplay between atom number and temperature as well as their fluctuations. Furthermore, by closing a classical feedback loop, we demonstrate the preparation of atomic ensembles with sub-poissonian shot-to-shot atom number fluctuations. Our results provide a novel testbed for observing thermodynamics and transport phenomena in mesosopic cold atomic gases and pave the way for cavity-assisted feedback stabilization of atom number and temperature in atomic quantum simulators.   

Live

How an open quantum system evolves in the presence of its environment is crucial to better understanding and improving many processes including the communication of quantum information and the transfer of energy. In the dissipative Markovian regime, energy or information lost by the system is never recovered, however, in the non-Markovian regime, recurrences of quantum properties such as coherences and entanglement can occur. Accurately modeling these recurrences could allow for improved experimental parameter estimation and for the potential control of noise processes in quantum technologies. Here, I will discuss reduced density matrix methods which extend the Kraus mapping formalism to capture non-Markovian dynamics using both classical and quantum computational resources. I will discuss application of these methods to molecular systems, with supporting data from IBM’s Qiskit simulator and devices.   

Live

Driven-dissipative quantum systems generically do not satisfy simple notions of detailed balance based on microscopic reversibility. We show that such systems can nonetheless have one or more hidden time-reversal symmetries, a concept that we define in terms of correlation functions and thermofield double states. We demonstrate that the presence of hidden symmetry directly leads to an extremely efficient method for analytically solving for steady states of the dynamics, even if such states are non-trivial. This represents a generalization of the so-called coherent quantum absorber method [1, 2]. We discuss how hidden TRS is relevant to a variety of driven qubit and nonlinear cavity models, and how this symmetry has simple, experimentally-observable consequences. We also discuss how this symmetry underlies somewhat opaque exact solution techniques in quantum optics that are based on phase space methods (i.e. the complex-P representation).

[1] K. Stannigel, P. Rabl, and P. Zoller, New J. Phys. 14, 063014 (2012).
[2] D. Roberts and A. Clerk, Phys. Rev. X 10 021022 (2020)   

Live

The physics of non-Hermitian systems is an active area of research. In a quantum setting, it is tempting to directly define the system’s state (i.e. its density matrix) from the Hamiltonian. While various prescriptions have been proposed (e.g. exponentiating the non-Hermitian Hamiltonian, occupying right eigenvectors), these are largely problematic. Further, a number of natural questions about non-Hermitian steady-states, such as the role of right and left eigenvectors, particle statistics or the sensitivity to boundary conditions analogous to the non-Hermitian skin effect have not been fully studied. Here, we address these issues in a more physical manner, using the fact that quantum non-Hermitian dynamics almost always requires a coupling to external dissipative environments. We study quantum versions of the paradigmatic Hatano-Nelson model (i.e. a non-Hermitian, non-reciprocal 1D tight binding model) that are realized using engineered dissipation, both for bosons and fermions. Our analysis reveals a number of basic and generic insights. In particular, we highlight the role of an emergent momentum-dependent temperature, and the fact that the non-Hermitian skin effect alone does not determine the steady-state sensitivity to boundary conditions.   

Live

Quantum many-body systems subjected to local measurements at a nonzero rate can be in distinct dynamical phases, with differing entanglement properties. We introduce theoretical approaches to measurement-induced phase transitions in "all-to-all" quantum circuits with unitaries and measurements, in which any qubit can couple to any other. We first solve the simplest "minimal cut" toy model for entanglement dynamics in all-to-all circuits. We then show that certain all-to-all measurement circuits allow exact results by exploiting the circuit's local tree-like structure, and we compare these results with numerics in all-to-all circuits. We characterize the two different phases in all-to-all circuits using observables that are sensitive to the amount of information propagated between the initial and final time.   

Live

Periodically-driven (Floquet) systems have been attracted much interest as one of the most important class of nonequilibium systems. Floquet-Magnus (FM) expansion is a powerful tool for Floquet systems under high-frequency drives. In closed Floquet systems, it gives an effective static Hamiltonian which describes their stroboscopic dynamics. However, in dissipative Floquet systems dominated by a Liouvillian, it remains an important problem whether the FM expansion gives a static effective Liouvillian (Liouvillianity).

We have made an answer for generic systems with local interactions. We have found that, while noninteracting systems can either preserve or break Liouvillianity of the FM expansion, generic interacting systems always show its breaking (Liouvillianity breaking), and that Liouvillianity breaking in such systems is essentially caused by the spread of interactions in FM expansions. Our results imply that generic interacting dissipative Floquet systems under Markovianity do not have static Markovian counterparts in high-frequency regimes, giving a sign of emergent non-Markovianity.

Reference:
K. Mizuta, K. Takasan, and N. Kawakami, arXiv:2008.13104 (2020)   

Live

In quantum optics, it is common to assume that atoms are point-like objects compared to the wavelength of the electromagnetic field they interact with. However, this dipole approximation is not always valid, e.g., if atoms couple to radiation at multiple discrete points. Previous work has shown that superconducting qubits coupled to a 1D waveguide can behave as such ‘giant atoms’ and then can interact through the waveguide without decohering, a phenomenon that is not possible with small atoms. In the present work, we prove that this decoherence-free interaction is also possible when the coupling to the waveguide is chiral. Furthermore, we derive conditions under which the giant atoms in this architecture exhibit dark states. In particular, we show that unlike small atoms, giant atoms in a chiral waveguide can reach a dark state even outside the driven-dissipative regime, i.e., without being excited by a coherent drive.   

Live

We study the non-equilibrium dynamics, including transport properties, of photons in the two-bath spin-boson model, in which a spin-1/2 particle is frustratingly coupled to two independent Ohmic bosonic baths. We show that the frustration in this model gives rise to rich physics in a wide range of energies, in contrast to the one-bath spin-boson model where the non-trivial physics occurs at an energy scale close to the renormalized spin frequency. The renormalized spin frequency in the two-bath spin-boson model is still important, featuring in different observables, including the elastic transport properties of a photon. The elastic scattering displays non-monotonic behavior at high frequencies, and is very different in the two channels: intra- and inter-bath scattering. The photon can also be inelastically scattered, a process in which it is split into several photons of smaller energies. We show that such inelastic processes are highly anisotropic, with the outgoing particles being preferentially emitted into only one of the baths. Moreover, the inelastic scattering rate is larger than in the one-bath case, and can exceed the total elastic rate. Our results can be verified with state-of-the-art circuit and cavity quantum electrodynamics experiments.

Reference: arXiv:2007.03690   

Live

In this work, we study temporal coarse-graining as a basis to derive accurate effective models for open quantum systems. In particular, we demonstrate that the coarse-graining time scale, when treated as a physical parameter, determines the validity of various commonly employed approximations such as the RWA and the Markov approximation. With a suitable choice of the coarse-graining time scale, we systemically derive the Lindblad dynamics without assuming the all-time factorizability of the full density matrix. Deviations from the Lindblad dynamics are quantified analytically and then compared to numerical results obtained from the full system-plus-reservoir master equation. We further compare the system-plus-reservoir approach to direct time-coarse-graining of the Lindblad master equation and to naïve time-averaging of the dynamical variables, emphasizing on the sources of their differences as well as the corresponding physical interpretations. Finally, we address the initial condition problem of time-coarse-grained dynamics and argue that the choice of the initial condition depends on one's interpretation of the physical nature of time-coarse-graining.   

Live

Symmetry-breaking transitions are a well-understood phenomenon of closed quantum systems in quantum optics, condensed matter, and high energy physics. However, symmetry breaking in open systems is less thoroughly understood, in part due to the richer steady-state and symmetry structure that such systems possess. For the prototypical open system---a Lindbladian---a unitary symmetry can be imposed in a "weak" or a "strong" way. We characterize the possible Z_n symmetry breaking transitions for both cases. In the case of Z_2, a weak-symmetry-broken phase guarantees at most a classical bit steady-state structure, while a strong-symmetry-broken phase admits a partially-protected steady-state qubit. Viewing photonic cat qubits through the lens of strong-symmetry breaking, we show how to dynamically recover the logical information after any gap-preserving strong-symmetric error; such recovery becomes perfect exponentially quickly in the number of photons. Our study forges a connection between driven-dissipative phase transitions and error correction.   

Live

Time-reversal symmetry is an intrinsic property of equilibrium systems that forbids currents under equilibrium conditions. On the other hand, time-reversal symmetry is explicitly broken in driven systems, leading to new states of matter. In this talk, I discuss the impact of time-reversal symmetry breaking on driven-dissipative systems. I will focus on the driven-dissipative Ising model, and show that a kind of spin current emerges in the non-equilibrium steady state. Interestingly, this current diverges at the critical point and shows nontrivial critical scaling with system size. While previous studies have concluded an effective equilibrium behavior at criticality, we find that the effective temperatures corresponding to two (longitudinal) components of the spin are equal in magnitude but opposite in sign, signaling the extreme non-equilibrium nature of the steady state. Finally, at the weakly dissipative critical point the current remains critical but exhibits new critical scaling. These features are immediately accessible in experimental platforms.   

Live

In the thermodynamic limit, the steady states of open quantum many-body systems can undergo nonequilibrium phase transitions due to a competition between Hamiltonian and dissipative terms. Here, we consider Markovian systems and elucidate structures of the Liouville super-operator that generates the dynamics. In many cases of interest, a non-orthogonal basis transformation can bring the Liouvillian into block-triangular form, making it possible to assess its spectrum. The spectral gap sets the asymptotic decay rate. The super-operator structure can be used to bound gaps from below, showing that, in a large class of systems, dissipative phase transitions are actually impossible and that the convergence to steady states is exponential. Furthermore, when the blocks on the diagonal are Hermitian, the Liouvillian spectra obey Weyl ordering relations. The results are exemplified by various spin models.

Reference: arXiv:2012.05505   

Live

Controlling the environment of a qubit to suppress decoherence is a key technique for modern quantum technologies. Such control can be either passive, via e.g. materials engineering, or active, via e.g. driving fields. Using a shallow defect center coupled to RF-driven surface spins, we demonstrate experimentally that spectral engineering of the spin bath enables improved qubit coherence. Results are in agreement with our quantitative model, and open the path to active decoherence protection using custom-designed waveforms applied to the environment rather than the qubit.