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It is shown that the group delay of an electron wave packet through a potential well can be either negative or positive and is tunable by finite electric fields. The group delay depends not only on the width of potential well and the incident energy, but also on the electric field strength. It is also proved that the transmission time and reflection time for two propagation directions satisfy reciprocal relation, resulting from the time reversal invariance in quantum mechanism.

In this work, we systematically investigate the group delay time of an electron wave packet through a two-dimensional semiconductor heterostructure. It is shown that the lateral displacement, resulting from the angular spread of the electron wave packet, plays an important role in total delay time. In the propagating case, the group delay time can be negative due to the effect of lateral displacement, and is greatly enhanced by transmission resonances. In the evanescent case, the delay time saturates to a constant in the opaque limit, which is simply the Hartman effect observed for a two-dimensional situation.

Achieving full control of a Bose-Einstein condensate can have valuable applications in metrology, quantum information processing, and quantum condensed matter physics. We propose protocols to simultaneously control the internal (related to its pseudospin-1/2) and motional (position-related) states of a spin-orbit-coupled Bose-Einstein condensate confined in a Morse potential. In the presence of synthetic spin-orbit coupling, the state transition of a noninteracting condensate can be implemented by Raman coupling and detuning terms designed by invariant-based inverse engineering. The state transfer may also be driven by tuning the direction of the spin-orbit-coupling field and modulating the magnitude of the effective synthetic magnetic field. The results can be generalized for interacting condensates by changing the time-dependent detuning to compensate for the interaction. We find that a two-level algorithm for the inverse engineering remains numerically accurate even if the entire set of possible states is considered. The proposed approach is robust against the laser-field noise and systematic device-dependent errors.

A finite-size quasi two-dimensional Bose-Einstein condensate collapses if the attraction between atoms is sufficiently strong. Here we present a theory of collapse for condensates with the interatomic attraction and spin-orbit coupling. We consider two realizations of spin-orbit coupling: the axial Rashba coupling and balanced, effectively one-dimensional, Rashba-Dresselhaus one. In both cases spin-dependent "anomalous" velocity, proportional to the spin-orbit coupling strength, plays a crucial role. For the Rashba coupling, this velocity forms a centrifugal component in the density flux opposite to that arising due to the attraction between particles and prevents the collapse at a sufficiently strong coupling. For the balanced Rashba-Dresselhaus coupling, the spin-dependent velocity can spatially split the initial state in one dimension and form spin-projected wavepackets, reducing the total condensate density. Depending on the spin-orbit coupling strength, interatomic attraction, and the initial state, this splitting either prevents the collapse or modifies the collapse process. These results show that the collapse can be controlled by a spin-orbit coupling, thus, extending the domain of existence of condensates of attracting atoms., Comment: 8 pages, 7 figures

The lateral displacement of electron beams transmitting through a two-dimensional semiconductor barrier is quite different from the prediction from Snell's law for electron waves. It is shown that the displacement can be greatly enhanced by transmission resonance when the incidence angle is less than but close to the critical angle for total reflection. The displacement depends not only on the barrier's thickness but also on the incidence angle and the incidence energy. The influence of electron's effective mass is also discussed. Theoretical results of the stationary-phase approach are confirmed by numerical simulations for a Gaussian-shaped incident beam. These phenomena may lead to novel applications in quantum electronic devices.

Conventional narrowband spectrum polarization devices are short but not robust, based on quasi-phase matching (QPM) technique, in periodically poled lithium niobate (PPLN) crystal. In this paper, we propose short-length and robust polarization rotators by using shortcuts to adiabaticity. Beyond the QPM condition, the electric field and period of PPLN crystal are designed in terms of invariant dynamics, and further optimized with respect to input wavelength/refractive index variations. In addition, the stability of conversion efficiency on the electric field and period of PPLN crystal is also discussed. As a consequence, the optimal shortcuts are fast as well as robust, which provide broadband spectrum polarization devices with short length.

The techniques of shortcuts to adiabaticity have been proposed to accelerate the “slow” adiabatic processes in various quantum systems with the applications in quantum information processing. In this paper, we study the counter-diabatic driving for fast adiabatic spin manipulation in a two-electron double quantum dot by designing time-dependent electric fields in the presence of spin-orbit coupling. To simplify implementation and find an alternative shortcut, we further transform the Hamiltonian in term of Lie algebra, which allows one to use a single Cartesian component of electric fields. In addition, the relation between energy and time is quantified to show the lower bound for the operation time when the maximum amplitude of electric fields is given. Finally, the fidelity is discussed with respect to noise and systematic errors, which demonstrates that the decoherence effect induced by stochastic environment can be avoided in speeded-up adiabatic control.

Graphene-assisted resonant transmission and enhanced Goos-Hänchen shift are investigated in a two-prism frustrated total internal reflection configuration. Due to the excitation of surface plasmons induced by graphene in a low terahertz frequency range, there exist the resonant transmission and anomalous Goos-Hänchen shifts in such an optical tunneling configuration. As compared to the case of the quantum well, a graphene sheet with unique optical properties can enhance the resonant transmission with a relatively low loss and modulate the large negative and positive Goos-Hänchen shifts by adjusting the chemical potential or electron relaxation time. These intriguing phenomena may lead to some potential applications in graphene-based electro-optic devices.

We analyze spin dynamics in the tunneling decay of a metastable localized state in the presence of spin-orbit coupling. We find that the spin polarization at short time scales is affected by the initial state while at long time scales both the probability- and the spin density exhibit diffraction-in-time phenomenon. We find that in addition to the tunneling time the tunneling in general can be characterized by a new parameter, the tunneling length. Although the tunneling length is independent on the spin-orbit coupling, it can be accessed by the spin rotation measurement., 6 pages, 7 figures

We apply an invariant-based inverse engineering method to control by time-dependent electric fields electron spin dynamics in a quantum dot with spin-orbit coupling in a weak magnetic field. The designed electric fields provide a shortcut to adiabatic processes that flips the spin rapidly, thus avoiding decoherence effects. This approach, being robust with respect to the device-dependent noise, can open new possibilities for the spin-based quantum information processing., 7 pages, 6 figures, with supplemental material. Errors in the published version have been corrected

We study effects of the shape of a two-dimensional waveguide on the spin-dependent electron transport in the presence of spin-orbit coupling. The transition from classical motion to the tunneling regime can be controlled there by modulating the strength of spin-orbit coupling if the waveguide has a constriction. The spin precession strongly depends on the shape of the waveguide., 3 pages, 3 figures

Diffraction in time (DIT) is a fundamental phenomenon in quantum dynamics due to time-dependent obstacles and slits. It is formally analogous to diffraction of light, and is expected to play an increasing role to design coherent matter wave sources, as in the atom laser, to analyze time-of-flight information and emission from ultrafast pulsed excitations, and in applications of coherent matter waves in integrated atom-optical circuits. We demonstrate that DIT emerges robustly in quantum waves emitted by an exponentially decaying source and provide a simple explanation of the phenomenon, as an interference of two characteristic velocities. This allows for its controllability and optimization., 4 pages, 6 figures

Motivated by recent time domain experiments on ultrafast atom ionization, we analyze the transients and timescales that characterize, besides the relatively long lifetime, the decay by tunneling of a localized state. While the tunneling starts immediately, some time is required for the outgoing flux to develop. This short-term behavior depends strongly on the initial state. For the initial state tightly localized so that the initial transients are dominated by over-the-barrier motion, the timescale for the flux propagation through the barrier is close to the B\"uttiker-Landauer traversal time. Then a quasistationary, slowly decay process follows, which sets ideal conditions for observing diffraction in time at longer times and distances. To define operationally a tunnelling time at the barrier edge, we extrapolate backwards the propagation of the wave packet escaped from the potential. This extrapolated time is considerably longer than the timescale of the flux and density buildup at the barrier edge., Comment: 9 pages, 10 figures

It is investigated that the lateral shifts of the ballistic electrons transmitted through a semiconductor quantum slabs can be negative as well as positive, which are analogous to the anomalous lateral shifts of the transmitted light beam through a dielectric slab. The necessary condition for the shift to be negative is advanced. It is shown that the lateral shifts depend not only on the structure parameters of semiconductor quantum slab, but also on the incidence angle and the incident energy. Numerical calculations further indicate that the lateral shifts can be tuned from negative to positive by the external applied electric field. The voltage-tunable lateral shifts may lead to potential applications in quantum electronic devices., Comment: 6 pages, 6 figures, submitted to J. Appl. Phys

We investigate the lateral displacements for ballistic electron beams in a two-dimensional electron gas modulated by metallic ferromagnetic (FM) stripes with parallel and antiparallel (AP) magnetization configurations. It is shown that the displacements are negative as well as positive, which can be controlled by adjusting the electric potential induced by the applied voltage and the magnetic field strength of FM stripes. Based on these phenomena, we propose an efficient way to realize a spin beam splitter, which can completely separate spin-up and spin-down electron beams in the AP configuration by their corresponding spatial positions.

Electronic transport is investigated in the asymmetric graphene superlattice consisting of a periodic potential structure and a wide potential barrier, which are separated by an internal potential well. Our results show that under a certain condition a pronounced peak occurs in the original transmission gap region, and reveal that such an asymmetric graphene superlattice containing a potential well can be equivalent to a double-barrier structure. Furthermore, the controllable potential depth and width of quantum well have significant effects on the transmission probability and electronic conductance. All these phenomena may lead to applications in various graphene-based electronic devices.

Tunable group delay and Hartman effect have been investigated for massless Dirac electrons in graphene magnetic barriers. In the presence of magnetic field, dwell time is found to be equal to net group delay plus the group delay contributing from the lateral shifts. The group delay times are discussed in both cases of normal and oblique incidence, to clarify the nature of Hartman effect. In addition, the group delay in transmission can be modulated from subluminality to superluminality by adjusting the magnetic field, which may also lead to potential applications in graphene-based microelectronics.

Tunneling times, including group delay and dwell time, are studied for massless Dirac electrons transmitting through a one-dimensional barrier in strain-engineered graphene. The Hartman effect, the independence of group delay on barrier length, is induced by the strain effect, and associated with the transmission gap and the evanescent mode. The influence of barrier height/length and strain modulus/direction on the group delay is also discussed, which provides the flexibility to control the group delay with applications in graphene-based devices. The relationship between group delay and dwell time is finally derived to clarify the nature of the Hartman effect.

The analogies between optical and electronic Goos-H\"{a}nchen effects are established based on electron wave optics in semiconductor or graphene-based nanostructures. In this paper, we give a brief overview of the progress achieved so far in the field of electronic Goos-H\"{a}nchen shifts, and show the relevant optical analogies. In particular, we present several theoretical results on the giant positive and negative Goos-H\"{a}nchen shifts in various semiconductor or graphen-based nanostructures, their controllability, and potential applications in electronic devices, e.g. spin (or valley) beam splitters.

We study electron transport in nanosized semiconductor waveguides of different shapes. The spin-dependent transport through these nonuniform nanostructures is investigated in the presence of spin-orbit coupling of the Rashba and Dresselhaus types. The resulting spin rotation strongly depends on the shape of the waveguide. The crossover from the classical motion to the tunneling regime can be controlled in the waveguide with narrowing by modulating the strength of the Rashba spin-orbit coupling.

We present a method relying on shortcuts to adiabaticity to achieve quantum detection of high frequency signals at the nanoscale in a robust manner. More specifically, our protocol delivers tailored amplitudes and frequencies for control fields that, firstly, enable the coupling of the sensor with high-frequency signals and, secondly, minimise errors that would otherwise spoil the detection process. To exemplify the method, we particularise to detection of signals emitted by fast-rotating nuclear spins with nitrogen vacancy center quantum sensors. However, our protocol is straightforwardly applicable to other quantum devices such as silicon vacancy centers, germanium vacancy centers, or divacancies in silicon carbide., Comment: 8 pages 2 figures

In the era of digital quantum computing, optimal digitized pulses are requisite for efficient quantum control. This goal is translated into dynamic programming, in which a deep reinforcement learning (DRL) agent is gifted. As a reference, shortcuts to adiabaticity (STA) provide analytical approaches to adiabatic speed up by pulse control. Here, we select single-component control of qubits, resembling the ubiquitous two-level Landau-Zener problem for gate operation. We aim at obtaining fast and robust digital pulses by combining STA and DRL algorithm. In particular, we find that DRL leads to robust digital quantum control with operation time bounded by quantum speed limits dictated by STA. In addition, we demonstrate that robustness against systematic errors can be achieved by DRL without any input from STA. Our results introduce a general framework of digital quantum control, leading to a promising enhancement in quantum information processing., 6 pages, 3 figures plus Supplemental Materials