We study the single-photon scattering along a one-dimensional cavity array with two distant two-level atoms in a supercavity,which aims to simulate a recent x-ray experiment [Nature 482,199（2012）].Without introducing dissipation,we find that when one atom is exactly located at a node of a mode of the supercavity and the other is at the antinode of that mode,no splitting of the reflectivity peak can appear.Nevertheless,the atom at the node significantly changes the positions of the reflectivity valleys.On the other hand,when the atom is shifted a little from the exact node,then the splitting can appear.We also explain these results with an analysis based on the general formal scattering theory.Our result implies the importance of non-resonant modes of the supercavity in our problem.
We provide a general dynamical approach for the quantum Zeno and anti-Zeno effects in an open quantum system under repeated non-demolition measurements. In our approach the repeated measurements are described by a general dynamical model without the wave function collapse postulation. Based on that model, we further study both the short-time and long-time evolutions of the open quantum system under repeated non-demolition measurements, and derive the measurement-modified decay rates of the excited state. In the cases with frequent ideal measurements at zero-temperature, we re-obtain the same decay rate as that from the wave function collapse postulation （Nature, 2000, 405： 546）. The correction to the ideal decay rate is also obtained under the non-ideal measurements. Especially, we find that the quantum Zeno and anti-Zeno effects are possibly enhanced by the non-ideal natures of measurements. For the open system under measurements with arbitrary period, we generally derive the rate equation for the long-time evolution for the cases with arbitrary temperature and noise spectrum, and show that in the long-time evolution the noise spectrum is effectively tuned by the repeated measurements. Our approach is also able to describe the quantum Zeno and anti-Zeno effects given by the phase modulation pulses, as well as the relevant quantum control schemes.
Energy is often partitioned into heat and work by two independent paths corresponding to the change in the eigenenergies or the probability distributions of a quantum system. The discrepancies of the heat and work for various quantum thermodynamic processes have not been well characterized in literature. Here we show how the work in quantum machines is differentially related to the isochoric, isothermal, and adiabatic processes. We prove that the energy exchanges during the quantum isochoric and isothermal processes are simply depending on the change in the eigenenergies or the probability distributions. However, for a time-dependent system in a non-adiabatic quantum evolution, the transitions between the different quantum states representing the quantum coherence can affect the essential thermodynamic properties, and thus the general definitions of the heat and work should be clarified with respect to the microscopic generic time-dependent system. By integrating the coherence effects in the exactly-solvable dynamics of quantum-spin precession, the internal energy is rigorously transferred as the work in the thermodynamic adiabatic process. The present study demonstrates that the quantum adiabatic process is sufficient but not necessary for the thermodynamic adiabatic process.
