A parity-time (PT )-symmetric system emerging from a quantum dynamics is highly desirable in order to understand the possible implications of PT symmetry in the next generation of quantum technologies.In this work, we address this need by proposing and studying a circuit-QED architecture that consists of two coupled resonators and two qubits (each coupled to one resonator).By means of external driving fields on the qubits, we are able to tune gains and losses in the resonators.Starting with the quantum dynamics of this system, we show the emergence of the PT symmetry via the selection of both driving amplitudes and frequencies.We engineer the system such that a non-number-conserving dipole-dipole interaction emerges, introducing an instability at large coupling strengths.The PT symmetry and its breaking, as well as the predicted instability in this circuit-QED system, can be observed in a transmission experiment.
A parity-time (PT )-symmetric system emerging from a quantum dynamics is highly desirable in order to understand the possible implications of PT symmetry in the next generation of quantum technologies.In this work, we address this need by proposing and studying a circuit-QED architecture that consists of two coupled resonators and two qubits (each coupled to one resonator).By means of external driving fields on the qubits, we are able to tune gains and losses in the resonators.Starting with the quantum dynamics of this system, we show the emergence of the PT symmetry via the selection of both driving amplitudes and frequencies.We engineer the system such that a non-number-conserving dipole-dipole interaction emerges, introducing an instability at large coupling strengths.The PT symmetry and its breaking, as well as the predicted instability in this circuit-QED system, can be observed in a transmission experiment.
We develop a rigorous theoretical framework for interaction-induced phenomena in the waveguide quantum electrodynamics (QED) driven by mechanical oscillations of the qubits. Specifically, we predict that the simplest setup of two qubits, harmonically trapped over an optical waveguide, enables the ultrastrong coupling regime of the quantum optomechanical interaction. Moreover, the combination of the inherent open nature of the system and the strong optomechanical coupling leads to emerging parity-time (PT) symmetry, quite unexpected for a purely quantum system without artificially engineered gain and loss. The PT phase transition drives long-living subradiant states, observable in the state-of-the-art waveguide QED setups.
In this work, a parity-time (PT)-symmetric system is investigated based on superconducting circuits, which allows the tunability of atom-atom coupling using superconducting qubits. The calculation results demonstrate that the interaction between artificial atoms significantly impacts the transmission spectrum and the conditions of the phase transition in the system. When introducing a weak probe signal into the PT-symmetric system, several findings are observed. (1) The symmetry and intensity of both the linear and nonlinear outputs can be fine-tuned by adjusting the coupling strength between artificial atoms or manipulating the gauge-invariant phase in the system. (2) Nonreciprocal transmission can be achieved by driving different cavity modes. (3) The exceptional point (EP) of the PT phase transition can be adjusted within a certain range by modifying the gauge-invariant phase or adjusting the coupling strength in the system. One feasible experimental setup is also described and analyzed based on existing experimental techniques. These findings may inspire further research into modulating quantum phase transitions based on superconducting circuits.
A Hamiltonian with Parity-Time (PT) symmetry can have fully real eigenvalues within its PT-symmetric regime. This is a special case in non-Hermitian quantum mechanics and has been widely used in open-system physics research. A pair of electromagnetically coupled parallel RLC resonant circuits, when incorporating a pair of equal-magnitude positive and negative resistances with equivalent gain (dissipation) strength, can form a PT-symmetric non-Hermitian system. This paper presents a teaching-oriented design and practical exploration of PT-symmetric physics research based on RLC resonant circuits. It also offers experimental studies on multilevel phase transitions resulting from the combination of PT symmetry and RLC resonance, enhancing the understanding of their characteristics.
Quantum dynamics of two XX interacting PT-symmetric non-Hermitian qubits: enhancement of quantum annealing
Quantum information platforms enable analog quantum simulations, such as quantum annealing, offering a promising route to solving complex combinatorial optimization problems. Here, we propose a quantum information architecture based on networks of interacting parity-time (PT)-symmetric non-Hermitian qubits. While the dynamics of individual PT-symmetric qubits have been experimentally demonstrated across multiple platforms including NV centers, superconducting circuits, and trapped-ion systems yet coherent dynamics in interacting systems remain largely unexplored. To address this issue we theoretically investigate stationary and time-dependent Hamiltonians relevant to quantum annealing using a minimal model of two interacting XX-coupled PT-symmetric non-Hermitian qubits. We analyze both symmetry-preserving and symmetry-broken regimes and demonstrate that adding even tiny PT-symmetric non-Hermitian terms in the qubits Hamiltonian allows to greatly enhance the probability of reaching the ground state after annealing.
More than a decade ago, it was shown that non-Hermitian Hamiltonians with combined parity (P) and time-reversal (T ) symmetry exhibit real eigenvalues over a range of parameters. Since then, the field of PT symmetry has seen rapid progress on both the theoretical and experimental fronts. These effective Hamiltonians are excellent candidates for describing open quantum systems with balanced gain and loss. Nature seems to be replete with examples of PT -symmetric systems; in fact, recent experimental investigations have observed the effects of PT symmetry breaking in systems as diverse as coupled mechanical pendula, coupled optical waveguides, and coupled electrical circuits. Recently, PT -symmetric Hamiltonians for tight-binding lattice models have been extensively investigated. Lattice models, in general, have been widely used in physics due to their analytical and numerical tractability. Perhaps one of the best systems for experimentally observing the effects of PT symmetry breaking in a one-dimensional lattice with tunable hopping is an array of evanescently-coupled optical waveguides. The tunneling between adjacent waveguides is tuned by adjusting the width of the barrier between them, and the imaginary part of the local refractive index provides the loss or gain in the respective waveguide. Calculating the time evolution of a wave packet on a lattice is relatively straightforward in the tight-binding model, allowing us to make predictions about the behavior of light propagating down an array of PT -symmetric waveguides. In this thesis, I investigate the the strength of the PT -symmetric phase (the region over which the eigenvalues are purely real) in lattices with a variety of PT - symmetric potentials. In Chapter 1, I begin with a brief review of the postulates of quantum mechanics, followed by an outline of the fundamental principles of PT - symmetric systems. Chapter 2 focuses on one-dimensional uniform lattices with a pair of PT -symmetric impurities in the case of open boundary conditions. I find that the PT phase is algebraically fragile except in the case of closest impurities, where the PT phase remains nonzero. In Chapter 3, I examine the case of periodic boundary conditions in uniform lattices, finding that the PT phase is not only nonzero, but also independent of the impurity spacing on the lattice. In addition, I explore the time evolution of a single-particle wave packet initially localized at a site. I find that in the case of periodic boundary conditions, the wave packet undergoes a preferential clockwise or counterclockwise motion around the ring. This behavior is quantified by a discrete momentum operator which assumes a maximum value at the PT -symmetry- breaking threshold. In Chapter 4, I investigate nonuniform lattices where the parity-symmetric hop- ping between neighboring sites can be tuned. I find that the PT phase remains strong in the case of closest impurities and fragile elsewhere. Chapter 5 explores the effects of the competition between localized and extended PT potentials on a lattice. I show that when the short-range impurities are maximally separated on the lattice, the PT phase is strengthened by adding short-range loss in the broad-loss region. Consequently, I predict that a broken PT symmetry can be restored by increasing the strength of the short-range impurities. Lastly, Chapter 6 summarizes my salient results and discusses areas which can be further developed in future research.
The concept of parity-time (PT) symmetry originates from the framework of quantum mechanics, where if the Hamiltonian operator satisfies the commutation relation with the parity and time operators, it shows real energy spectrum. Recently, PT symmetry was introduced into various systems, such as optics, electronic circuits, acoustics, and other classical fields to further study the dynamical behaviors of the Hamiltonian and the energies. To focus on the dynamical evolution of the quantum state, here we experimentally studied the dynamical evolution of a two-level quantum system under the PT symmetric Hamiltonian using single-photon system. By enlarging the system using ancillary qubit and encoding the subsystem under the non-Hermitian Hamiltonian with post-selection, the evolution of the state can be characterized with a high fidelity. Owing to the effectively operation of the dilation method, our work provides a route for further exploiting the exotic properties of PT symmetric Hamiltonian for quantum simulation and quantum information processing.