Controlling nonequilibrium properties of quantum systems holds the key to many promising quantum technologies. Here I'll introduce the power of symmetry as a resource to manipulate quantum Non-Equilibrium Steady States (NESS). In the first part of the talk I'll introduce some preliminaries about the role of symmetries in steady state quantum transport and how this concept can be exploited to control quantum currents. I’ll introduce a novel scheme to identify symmetries in presence of a weak disorder. The scheme will identify key signatures in the dynamical quantum currents that are unique to symmetric systems and give us vital information about the underlying molecular symmetries. In the second part, I'll introduce magnetic fields that can be used to break the open system symmetries in single-particle simple cubic lattices. In the absence of a magnetic field the open system symmetries are preserved and help modulate the NESS based on the symmetry decomposition of the initial state. The presence of a magnetic field breaks symmetries in preferential directions with all symmetries being broken only in the presence of an anisotropic field. These results demonstrate the importance of symmetry not only as an organizing principle in physics but also as a tool to control quantum systems.
Controlling nonequilibrium properties of quantum systems holds the key to many promising quantum technologies. Here I'll introduce the power of symmetry as a resource to manipulate quantum Non-Equilibrium Steady States (NESS). In the first part of the talk I'll introduce some preliminaries about the role of symmetries in steady state quantum transport and how this concept can be exploited to control quantum currents. I’ll introduce a novel scheme to identify symmetries in presence of a weak disorder. The scheme will identify key signatures in the dynamical quantum currents that are unique to symmetric systems and give us vital information about the underlying molecular symmetries. In the second part, I'll introduce magnetic fields that can be used to break the open system symmetries in single-particle simple cubic lattices. In the absence of a magnetic field the open system symmetries are preserved and help modulate the NESS based on the symmetry decomposition of the initial state. The presence of a magnetic field breaks symmetries in preferential directions with all symmetries being broken only in the presence of an anisotropic field. These results demonstrate the importance of symmetry not only as an organizing principle in physics but also as a tool to control quantum systems.
Symmetry is a powerful concept in physics, and its recent application to understand nonequilibrium behavior is providing deep insights and groundbreaking exact results. Here we show how to harness symmetry to control transport and statistics in open quantum systems. Such control is enabled by a first-order-type dynamic phase transition in current statistics and the associated coexistence of different transport channels (or nonequilibrium steady states) classified by symmetry. Microreversibility then ensues, via the Gallavotti-Cohen fluctuation theorem, a twin dynamic phase transition for rare current fluctuations. Interestingly, the symmetry present in the initial state is spontaneously broken at the fluctuating level, where the quantum system selects the symmetry sector that maximally facilitates a given fluctuation. We illustrate these results in a qubit network model motivated by the problem of coherent energy harvesting in photosynthetic complexes, and introduce the concept of a symmetry-controlled quantum thermal switch, suggesting symmetry-based design strategies for quantum devices with controllable transport properties.
Controlling transport in quantum systems holds the key to many promising quantum technologies. Here we review the power of symmetry as a resource to manipulate quantum transport and apply these ideas to engineer novel quantum devices. Using tools from open quantum systems and large deviation theory, we show that symmetry-mediated control of transport is enabled by a pair of twin dynamic phase transitions in current statistics, accompanied by a coexistence of different transport channels. By playing with the symmetry decomposition of the initial state, one can modulate the importance of the different transport channels and hence control the flowing current. Motivated by the problem of energy harvesting, we illustrate these ideas in open quantum networks, an analysis that leads to the design of a symmetry-controlled quantum thermal switch. We review an experimental setup recently proposed for symmetry-mediated quantum control in the lab based on a linear array of atom-doped optical cavities, and the possibility of using transport as a probe to uncover hidden symmetries, as recently demonstrated in molecular junctions, is also discussed. Other symmetry-mediated control mechanisms are also described. Overall, these results demonstrate the importance of symmetry not only as an organizing principle in physics but also as a tool to control quantum systems.
Symmetries play a pivotal role in our understanding of the properties of quantum many-body systems. While there are theorems and a well-established toolbox for systems in thermal equilibrium, much less is known about the role of symmetries and their connection to dynamics out of equilibrium. This arises due to the direct link between a system’s thermal state and its Hamiltonian, which is generally not the case for nonequilibrium dynamics. Here we present a pathway to identify the effective symmetries and to extract them from data in nonequilibrium quantum many-body systems. Our approach is based on exact relations between correlation functions involving different numbers of spatial points, which can be viewed as nonequilibrium versions of (equal-time) Ward identities encoding the symmetries of the system. We derive symmetry witnesses, which are particularly suitable for the analysis of measured or simulated data at different snapshots in time. To demonstrate the potential of the approach, we apply our method to numerical and experimental data for a spinor Bose gas. We investigate the important question of a dynamical restoration of an explicitly broken symmetry of the Hamiltonian by the initial state. Remarkably, it is found that effective symmetry restoration can occur long before the system equilibrates. We also use the approach to define and identify spontaneous symmetry breaking far from equilibrium, which is of great relevance for applications to nonequilibrium phase transitions. Our work opens new avenues for the classification and analysis of quantum as well as classical many-body dynamics in a large variety of systems, ranging from ultracold quantum gases to cosmology.
In classical settings, the Mpemba effect occurs when a hotter system cools faster than an initially colder one. In quantum systems, this effect can be reinterpreted exploiting the concept of symmetries, with the asymmetry of a subsystem playing the role of temperature. A quantum Mpemba effect arises when a more asymmetric state restores the symmetry faster than a less asymmetric one. Previous work mainly focuses on closed systems characterized by thermal equilibration and Hamiltonian symmetries. In this paper, we analyze the dynamics of asymmetry in an open quantum many-body system featuring symmetry breaking and uncover dynamical behavior that appears to be unique to these settings. In the symmetric phase, we demonstrate the existence of a quantum Mpemba effect, which emerges as a direct consequence of a non-monotonic evolution of the asymmetry. In the broken-symmetry phase, we analyze the imbalance between the system's ability to increase or to decrease its asymmetry. Our results extend the notion of quantum Mpemba effects to open quantum many-body systems exhibiting symmetry-breaking phase transitions and establish them as a platform for observing and controlling anomalous relaxation phenomena.
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.
High-harmonic generation (HHG) in inversion-symmetric systems is typically restricted to odd harmonics by symmetry. Here, we show that this selection rule can be broken without modifying the underlying Hamiltonian. We investigate a boundary-driven Su-Schrieffer-Heeger (SSH) chain coupled to source and sink reservoirs and demonstrate that dissipative dynamics generates a nonequilibrium steady state carrying a finite DC current. While the SSH Hamiltonian retains inversion symmetry, the current-carrying steady-state density matrix does not, leading to the emergence of even harmonics in the emitted spectrum. Using a correlation-matrix approach based on the Lindblad master equation, we obtain the steady state and calculate the resulting HHG response. We find that the intensity of the even harmonics is directly controlled by the transport current, establishing a link between nonequilibrium charge transport and HHG selection rules. Our results uncover a mechanism for even-harmonic generation that relies solely on nonequilibrium steady-state symmetry breaking and provide a route to probing transport currents through ultrafast nonlinear spectroscopy in centrosymmetric quantum systems.