We put forward several inherently quantum characteristics of the dwell time, and propose an operational method to detect them. The quantum dwell time is pointed out to be a conserved quantity, totally bypassing Pauli's theorem. Furthermore, the quantum dwell time in a region for one dimensional motion is doubly degenerate. In presence of a potential barrier, the dwell time becomes bounded, unlike the classical quantity. By using off-resonance coupling to a laser we propose an operational method to measure the absorption by a complex potential, and thereby the average time spent by an incoming atom in the laser region.
Relation between quantum dwell times and flux-flux correlations
我们研究量子粒子在空间区域中的停留时间与边界处的通量-通量相关性之间的联系。本文证明了磁通-磁通关联函数的一阶矩和二阶矩的存在性，从而推广了Pollak和Miller [E. Pollak和W. H. Miller，Phys. Rev. Lett. { \bf 53}，115（1984）]，与驻留时间分布的相应矩一致，而三阶和更高阶矩则不一致。我们还讨论了操作方法和近似测量的通量通量关联函数，从而二阶矩的停留时间，这被证明是特征量子，大于相应的经典时刻，即使是自由移动的粒子。
The dwell time is calculated within the framework of time dependent weak measurement considering dissipative interaction between a spin half system and the environment. Caldirola and Montaldi's method of retarded Schroedinger equation is used to study the dissipative system. The result shows that inclusion of dissipative interaction prevents zero time tunneling.
A number of approaches to the problem of defining arrival and dwell time probabilities in quantum theory make use of idealised models of clocks. An interesting question is the extent to which the probabilities obtained in this way are related to standard semiclassical results. In this paper we explore this question using a reasonably general clock model, solved using path integral methods. We find that in the weak coupling regime where the energy of the clock is much less than the energy of the particle it is measuring, the probability for the clock pointer can be expressed in terms of the pro…
Dwell time for a two state particle tunneling through a noisy thermal magnetic barrier has been calculated by studying the time evolution of the system. The effect of temperature has been included by averaging over the environmental magnetic modes. The time scale has been calculated in the framework of weak measurement. The dwell time initially increases with the rise of temperature and finally saturates. The increment of dwell time can be explained by the phenomena of quantum memory loss caused by efficient energy exchange with the environmental modes. The saturation region at higher temperat…
The tunneling time through an arbitrary bounded one-dimensional barrier is investigated using the dwell time operator. We relate the tunneling time to the conditioned average of the dwell time operator because of the natural post-selection in the case of successful tunneling. We discuss an indirect measurement by timing the particle, and show we are able to reconstruct the conditioned average value of the dwell time operator by applying the contextual values formalism for generalized measurements based on the physics of Larmor precession. The experimentally measurable tunneling time in the wea…
The lifetime of an unstable state or resonance formed as an intermediate state in two body scattering is known to be related to the dwell time or the time spent within a given region of space by the two interacting particles. This concept is extended to the case of three body systems and a relation connecting the three body dwell time with the two body dwell times of the substructures of the three body system is derived for the case of separable wave functions. The Kapur Peierls formalism is revisited to discover one of the first definitions of dwell time in literature. An extension of the Kap…
The dwell time for dissipative quantum system is shown to increase with barrier width. It clearly precludes Hartman effect for dissipative systems. Here calculation has been done for inverted parabolic potential barrier.
We study the energy properties of a particle in one dimensional semi-harmonic rectangular wells and barriers. The integration of energies is obtained by solving a simple transcendental equation. Scattering states are shown to include cases in which the impinging particle is 'captured' by the semi-harmonic rectangular potentials. The 'time of capture' is connected with the dwell time of the scattered wave. Using the particle absorption method, it is shown that the dwell time $τ^a_D$ coincides with the phase time $τ_W$ of Eisenbud and Wigner, calculated as the energy derivative of the reflected …
Measurements of current-voltage (I-V) characteristics of a high quality Al/Al$_2$O$_3$/Al junction at temperatures ranging from 3.5 K to 300 K have been used to extract the barrier properties. Fitting results using Simmons' model led to a constant value of barrier width $s$$\sim$20.8~$\textrmÅ$ and a continuous increase in the barrier height with decreasing temperature. The latter is used to determine the energy band gap temperature dependence and average phonon frequency $ω$ = 2.05 $\times$ 10$^{13}$ sec$^{-1}$ in Al$_2$O$_3$, which adds confidence to the precision of our measurements. The ba…
We develop a new quantum-mechanical approach to scattering a particle on a one-dimensional (1D) system of two identical rectangular potential barriers, which implies modelling the dynamics of its subprocesses -- transmission and reflection -- at all stages of scattering. On its basis we define, for each subprocess, the dwell time as well as the local (exact) and asymptotic (extrapolated) group times. Our concept of the asymptotic transmission group time confirms the validity of the Wigner phase time in the opaque limit, as well as the existence of the usual and generalized Hartman effects pred…
The average dwell time of an electron in a potential barrier formed by an external electric field and the potential of a helium atom is evaluated within a semi classical one-dimensional tunneling approach. The tunneling electron is considered to interact with a nuclear charge screened by the electron in the helium ion. It is found that screening leads to smaller average dwell times of the tunneling electron. The dissipative effect of the environment on the tunneling electron is taken into account within a semiclassical model involving a velocity dependent frictional force and is found to chang…
In this paper, we calculate the quantum time delays for neutron scattering off the Earth's linear gravitational potential. The quantum time delays are obtained by subtracting the classical returning time (CRT) from the Wigner time, the dwell time and the redefined Larmor time respectively. Different from the conventional definition, our Larmor time is defined by aligning the magnetic field along the neutron propagation direction, and this definition does give reasonable results for motions through a free region and a square barrier. It is worth noting that in the zero magnetic field limit, the…
We present in this work an analysis of the damage imposed by the atom on the field state inside a lossy superconducting cavity. To access such effects, we propose two procedures to preserve a qubit of the decay effects of an imperfect quantum memory: the first by means of an quasi-instantaneous phase kick applied in the atom, and the second by means of controlled resonant and dispersive interactions. We immediately demonstrate that, in both procedures, the dwell time of the qubit in the cavity increases significantly, being expressively higher for the second. A relation between the inaccuracy …
We present a new model of scattering a quantum particle on the potential step, which reconstructs the prehistory of the subensembles of transmitted and reflected particles by their final states. Unlike the conventional one this model predicts the existence of a transitional spatial region behind the potential step where the probability to find reflected particles is nonzero and the average velocity of transmitted particles monotonously varies between asymptotic values. For both subprocesses we define the dwell and asymptotic group times.
Characteristic features of tunneling times for dissipative tunneling of a particle through a rectangular barrier are studied within a semiclassical model involving dissipation in the form of a velocity dependent frictional force. The average dwell time and traversal time with dissipation are found to be less than those without dissipation. This counter-intuitive behaviour is reversed if one evaluates the physically relevant transmission dwell time. Apart from these observations, we find that the percentage of energy lost by the tunneling particle is higher for smaller energies. The above obser…
