Geometric phases along quantum trajectories
arXiv:2301.04222 · doi:10.22331/q-2023-06-02-1029
Abstract
A monitored quantum system undergoing a cyclic evolution of the parameters governing its Hamiltonian accumulates a geometric phase that depends on the quantum trajectory followed by the system on its evolution. The phase value will be determined both by the unitary dynamics and by the interaction of the system with the environment. Consequently, the geometric phase will acquire a stochastic character due to the occurrence of random quantum jumps. Here we study the distribution function of geometric phases in monitored quantum systems and discuss when/if different quantities, proposed to measure geometric phases in open quantum systems, are representative of the distribution. We also consider a monitored echo protocol and discuss in which cases the distribution of the interference pattern extracted in the experiment is linked to the geometric phase. Furthermore, we unveil, for the single trajectory exhibiting no quantum jumps, a topological transition in the phase acquired after a cycle and show how this critical behavior can be observed in an echo protocol. For the same parameters, the density matrix does not show any singularity. We illustrate all our main results by considering a paradigmatic case, a spin-1/2 immersed in time-varying a magnetic field in presence of an external environment. The major outcomes of our analysis are however quite general and do not depend, in their qualitative features, on the choice of the model studied.
arXiv comment20 pages, 15 figures
References in corpus (55)
- Non-Abelian Anyons and Topological Quantum Computation
- Holonomic Quantum Computation
- Quantum trajectories and open many-body quantum systems
- Open Quantum Systems. An Introduction
- Geometric quantum computation with NMR
- Geometric phases for mixed states in interferometry
- Random Quantum Circuits
- Observing single quantum trajectories of a superconducting qubit
- Observation of Berry's Phase in a Solid State Qubit
- Detection of Geometric Phases in Superconducting Nanocircuits
- Observation of quantum jumps in a superconducting artificial atom
- Implementation of universal quantum gates based on nonadiabatic geometric phases
- Experimental Realization of Non-Abelian Geometric Gates
- Kinematic approach to the mixed state geometric phase in nonunitary evolution
- Non-adiabatic conditional geometric phase shift with NMR
- Geometric phase in open systems
- Quantum Adiabatic Markovian Master Equations
- Continuous quantum error correction via quantum feedback control
- Berry phase for a spin 1/2 in a classical fluctuating field
- Adiabatic approximation in open quantum systems
- Off-Diagonal Geometric Phases
- Experimental implementation of universal nonadiabatic geometric quantum gates in a superconducting circuit
- Geometric phases for non-degenerate and degenerate mixed states
- Experimental determination of the Berry phase in a superconducting charge pump
- Geometric nature of the environment-induced Berry phase and geometric dephasing
- Berry phase in a non-isolated system
- Generalization of geometric phase to completely positive maps
- Exploring the Effect of Noise on the Berry Phase
- Adiabaticity in open quantum systems
- Continuous-variable geometric phase and its manipulation for quantum computation in a superconducting circuit
- Off-diagonal geometric phase for mixed states
- Geometric phases in open systems: an exact model to study how they are corrected by decoherence
- Geometric phase with nonunitary evolution in presence of a quantum critical bath
- Improving quantum annealing of the ferromagnetic -spin model through pausing
- Adiabatic Approximation for weakly open systems
- Phases of quantum states in completely positive non-unitary evolution
- Synchronization along quantum trajectories
- Adiabatic Markovian Dynamics
- Measuring the Berry Phase in a Superconducting Phase Qubit by a Shortcut to Adiabaticity
- Geometric phase for open quantum systems and stochastic unravellings
- Effective Hamiltonian approach to adiabatic approximation in open systems
- Approach to realizing nonadiabatic geometric gates with prescribed evolution paths
- Topological transition in measurement-induced geometric phases
- Path-optimized nonadiabatic geometric quantum computation on superconducting qubits
- Observing a Topological Transition in Weak-Measurement-Induced Geometric Phases
- Measurement of a Vacuum-Induced Geometric Phase
- Quantum trajectories for time-dependent adiabatic master equations
- Corrections to the Berry phase in a solid-state qubit due to low-frequency noise
- Weak-measurement-induced asymmetric dephasing: manifestation of intrinsic measurement chirality
- On geometric phases for quantum trajectories
- Weak-measurement-induced phases and dephasing: broken symmetry of the geometric phase
- Hidden parameters in open-system evolution unveiled by geometric phase
- Transitionless quantum driving in spin echo
- Quantum state diffusion, measurement and second quantization
- Quantum thermodynamics under continuous monitoring: a general framework