Dynamical quantum phase transition in XY chains with the Dzyaloshinskii-Moriya and XZY-YZX three-site interactions

We study the dynamical quantum phase transitions (DQPTs) in the XY chains with the Dzyaloshinskii-Moriya interaction and the XZY-YZX type of three-site interaction after a sudden quench. Both the models can be mapped to the spinless free fermion models by the Jordan-Wigner and Bogoliubov transformations with the form $H=\sum_{k}\varepsilon_{k}(\eta^†_{k}\eta_{k}-\frac{1}{2})$, where the quasiparticle excitation spectra $\varepsilon_{k}$ may be smaller than 0 for some $k$ and are asymmetrical ($\varepsilon_{k}\neq\varepsilon_{-k}$). It's found that the factors of Loschmidt echo equal 1 for some $k$ corresponding to the quasiparticle excitation spectra of the pre-quench Hamiltonian satisfying $\varepsilon_{k}\cdot\varepsilon_{-k}<0$, when the quench is from the gapless phase. By considering the quench from different ground states, we obtain the conditions for the occurrence of DQPTs for the general XY chains with gapless phase, and find that the DQPTs may not occur in the quench across the quantum phase transitions regardless of whether the quench is from the gapless phase to gapped phase or from the gapped phase to gapless phase. This is different from the DQPTs in the case of quench from the gapped phase to gapped phase, in which the DQPTs will always appear. Besides, we also analyze the different reasons for the absence of DQPTs in the quench from the gapless phase and the gapped phase. The conclusion can also be extended to the general quantum spin chains.

Measuring Loschmidt echo via Floquet engineering in superconducting circuits

The Loschmidt echo is a useful diagnostic for the perfection of quantum time-reversal process and the sensitivity of quantum evolution to small perturbations. The main challenge for measuring the Loschmidt echo is the time reversal of a quantum evolution. In this work, we demonstrate the measurement of the Loschmidt echo in a superconducting 10-qubit system using Floquet engineering and discuss the imperfection of an initial Bell-state recovery arising from the next-nearest-neighbour (NNN) coupling present in the qubit device. Our results show that the Loschmidt echo is very sensitive to small perturbations during quantum-state evolution, in contrast to the quantities like qubit population that is often considered in the time-reversal experiment. These properties may be employed for the investigation of multiqubit system concerning many-body decoherence and entanglement, etc., especially when devices with reduced or vanishing NNN coupling are used.

Effects of time on the evolution of a wave packet in the tunneling dynamics

We investigate the time-dependent electron wave packet in a one-dimensional geometry with the potential bent by a homogeneous external field. Based on the behaviors of the wave packet over time, we observe a crossover time. After this crossover time, the temporal evolution of the wave packet comes into a new regime, where the wave packet evolves in a self-similar structure. To establish the time scale of this crossover quantitatively, we utilize the Loschmidt Echo function, through which the time at which the crossover occurs can be extracted. We also find the time of the maximum ionization velocity can be comparable with the semi-classical tunneling delay time.

Isospectral Twirling and Quantum Chaos

We show that the most important measures of quantum chaos, such as frame potentials, scrambling, Loschmidt echo and out-of-time-order correlators (OTOCs), can be described by the unified framework of the isospectral twirling, namely the Haar average of a k-fold unitary channel. We show that such measures can then always be cast in the form of an expectation value of the isospectral twirling. In literature, quantum chaos is investigated sometimes through the spectrum and some other times through the eigenvectors of the Hamiltonian generating the dynamics. We show that thanks to this technique, we can interpolate smoothly between integrable Hamiltonians and quantum chaotic Hamiltonians. The isospectral twirling of Hamiltonians with eigenvector stabilizer states does not possess chaotic features, unlike those Hamiltonians whose eigenvectors are taken from the Haar measure. As an example, OTOCs obtained with Clifford resources decay to higher values compared with universal resources. By doping Hamiltonians with non-Clifford resources, we show a crossover in the OTOC behavior between a class of integrable models and quantum chaos. Moreover, exploiting random matrix theory, we show that these measures of quantum chaos clearly distinguish the finite time behavior of probes to quantum chaos corresponding to chaotic spectra given by the Gaussian Unitary Ensemble (GUE) from the integrable spectra given by Poisson distribution and the Gaussian Diagonal Ensemble (GDE).