We propose a class of schemes for robust population transfer between quantum states that utilize trains of coherent pulses and represent a generalized adiabatic passage via a wave packet. We study piecewise Stimulated Raman Adiabatic Passage with pulse-to-pulse amplitude variation, and piecewise chirped Raman passage with pulse-to-pulse phase variation, implemented with an optical frequency comb. In the context of production of ultracold ground-state molecules, we show that with almost no knowledge of the excited potential, robust high-efficiency transfer is possible
The time evolution of periodically driven non-Hermitian systems is in general non-unitary but can be stable. It is hence of considerable interest to examine the adiabatic following dynamics in periodically driven non-Hermitian systems. We show in this work the possibility of piecewise adiabatic following interrupted by hopping between instantaneous system eigenstates. This phenomenon is first observed in a computational model and then theoretically explained, using an exactly solvable model, in terms of the Stokes phenomenon. In the latter case, the piecewise adiabatic following is shown to be…
We develop a method for executing robust and selective transfer of populations between a single level and pre-selected superpositions of energy eigenstates. Viewed in the frequency domain, our method amounts to executing a series of simultaneous adiabatic passages into each component of the target superposition state. Viewed in {the} time domain, the method works by accumulating the wavefunction of the target wave packet as it revisits the Franck Condon region, in what amounts to an extension of the Piecewise Adiabatic Passage technique [ Shapiro et.al., Phys. Rev. Lett. 99, 033002 (2007)] to …
In this work, we propose a method to create an atomic frequency comb (AFC) in hot atomic vapors using the piecewise adiabatic passage (PAP) technique. Due to the Doppler effect, the trains of pulses used for PAP give rise to a velocity-dependent transfer of the atomic population from the initial state to the target one, thus forming a velocity comb whose periodicity depends not only on the repetition rate of the applied pulses but also on the specific atomic transitions considered. We highlight the advantages of using this transfer technique with respect to standard methods and discuss, in par…
We demonstrate a method of adiabatic population transfer from a single quantum state into a coherent superposition of states. The transfer is executed with femtosecond pulses, spectrally shaped in simple and intuitive manner, which does not require iterative feedback-controlled loops. In contrast to non-adiabatic methods of excitation, our approach is not sensitive to the exact value of laser intensity. We show that the population transfer is complete, and analyze the possibility of controlling the relative phases and amplitudes of the excited eigenstates. We discuss the limitations of the pro…
The dynamics of a periodically driven system whose time evolution is governed by the Schrödinger equation with non-Hermitian Hamiltonians can be perfectly stable. This finding was only obtained very recently and will be enhanced by many exact solutions discovered in this work. The main concern of this study is to investigate the adiabatic following dynamics in such non-Hermitian systems stabilized by periodic driving. We focus on the peculiar behaviour of stable cyclic (Floquet) states in the slow-driving limit. It is found that the stable cyclic states can either behave as intuitively expecte…
Resonant dissipation-enabled adiabatic quantum state transfer processes between the polarization degrees of freedom of a single photon wave packet and quantum emitters are discussed. These investigations generalize previous work [N. Trautmann and G. Alber, Phys. Rev. A 93, 053807 (2015)] by taking into account the properties of the spontaneously emitted photon wave packet and of non adiabatic corrections. It is demonstrated that the photonic degrees of freedoms of these adiabatic one-photon quantum state transfer processes can be used for the passive, heralded and deterministic preparation of …
Optimal control problem with a goal to squeeze wave packet of a trapped quantum particle is considered and solved analytically using adiabatic approximation. The analytical solution that drives the particle into a highly localized final state is presented for a case of an infinite well trapping potential. The presented solution may be applied to increase the resolution of atom lithography.
A model of the asymmetric coherent scattering process (caused by initial atomic wave-packet splitting in the momentum space) taking place at the large detuning and adiabatic course of interaction for an effective two-state system interacting with a standing wave of laser radiation is discussed. We show that the same form of initial wave-packet splitting may lead to different, in general, diffraction patterns for opposite, adiabatic and resonant, regimes of the standing-wave scattering. We show that the scattering of the Gaussian wave packet in the adiabatic case presents refraction (a limiting…
Trajectory-based mixed quantum-classical approaches to coupled electron-nuclear dynamics suffer from well-studied problems such as the lack of (or incorrect account for) decoherence in the trajectory surface hopping method and the inability of reproducing the spatial splitting of a nuclear wave packet in Ehrenfest-like dynamics. In the context of electronic non-adiabatic processes, these problems can result in wrong predictions for quantum populations and in unphysical outcomes for the nuclear dynamics. In this paper we propose a solution to these issues by approximating the coupled electronic…
We experimentally demonstrate and systematically study the stimulated revival (echo) of motional wave packet oscillations. For this purpose, we prepare wave packets in an optical lattice by non-adiabatically shifting the potential and stimulate their reoccurence by a second shift after a variable time delay. This technique, analogous to spin echoes, enables one even in the presence of strong dephasing to determine the coherence time of the wave packets. We find that for strongly bound atoms it is comparable to the cooling time and much longer than the inverse of the photon scattering rate.
We explain the concept of superadiabatic approximations and show how in the context of the Born- Oppenheimer approximation they lead to an explicit formula that can be used to predict transitions at avoided crossings. Based on this formula, we present a simple method for computing wave packet dynamics across avoided crossings. Only knowledge of the adiabatic electronic energy levels near the avoided crossing is required for the computation. In particular, this means that no diabatization procedure is necessary, the adiabatic energy levels can be computed on the fly, and they only need to be co…
Shortcuts to adiabaticity have been proposed to speed up the "slow" adiabatic transport of an atom or a wave packet of atoms. However, the freedom of the inverse engineering approach with appropriate boundary conditions provides thousands of trap trajectories for different purposes, for example, time and energy minimizations. In this paper, we propose trigonometric protocols for fast and robust atomic transport, taking into account cubic or quartic anharmonicities. The numerical results have illustrated that such trigonometric protocols, particular cosine ansatz, is more robust and the corresp…
We numerically investigate the performance of atomic transport in optical microtraps via the so called spatial adiabatic passage technique. Our analysis is carried out by means of optimal control methods, which enable us to determine suitable transport control pulses. We investigate the ultimate limits of the optimal control in speeding up the transport process in a triple well configuration for both a single atomic wave packet and a Bose-Einstein condensate within a regime of experimental parameters achievable with current optical technology.
Readout and retrieval processes are proposed for efficient, high-fidelity quantum state transfer between a matter qubit, encoded in the level structure of a single atom or ion, and a photonic qubit, encoded in a time-reversal-symmetric single-photon wave packet. They are based on controlling spontaneous photon emission and absorption of a matter qubit on demand in free space by stimulated Raman adiabatic passage. As these processes do not involve mode selection by high-finesse cavities or photon transport through optical fibers, they offer interesting perspectives as basic building blocks for …
Using numerical simulations of two-photon electronic absorption with femtosecond pulses in Na$_2$ we show that: i) it is possible to avoid the characteristic saturation or dumped Rabi oscillations in the yield of absorption by time-delaying the laser pulses; ii) it is possible to accelerate the onset of adiabatic passage by using the vibrational coherence starting in a wave packet; and iii) it is possible to prepare the initial wave packet in order to achieve full state-selective transitions with broadband pulses. The findings can be used, for instance, to achieve ultrafast adiabatic passage b…
We propose a simple scheme capable of adiabatically splitting an atomic wave packet using two independent translating traps. Implemented with optical dipole traps, our scheme allows a high degree of flexibility for atom interferometry arrangements and highlights its potential as an efficient and high fidelity atom optical beam splitter.
We show how the Laplace transform can be used to give a solution of the time-dependent Schrödinger equation for an arbitrary initial wave packet if the solution of the stationary equation is known. The solution is obtained without summing up eigenstates nor do we need the path integral. We solve the initial value problem for three characteristic piecewise constant potentials. The results give an intuitive picture of the wave packet dynamics, reproducing explicitly all possible reflection and transmission processes. We investigate classical and quantum properties of the evolution and determine …
Performing a faithful transfer of an unknown quantum state is a key challenge for enabling quantum networks. The realization of networks with a small number of quantum links is now actively pursued, which calls for an assessment of different state transfer methods to guide future design decisions. Here, we theoretically investigate quantum state transfer between two distant qubits, each in a cavity, connected by a waveguide, e.g., an optical fiber. We evaluate the achievable success probabilities of state transfer for two different protocols: standard wave packet shaping and adiabatic passage.…
The scattering of 1D matter wave bright solitons on attractive potentials enables one to populate bound states, a feature impossible with noninteracting wave packets. Compared to noninteracting states, the populated states are renormalized by the attractive interactions between atoms and keep the same topology. This renormalization can even transform a virtual state into a bound state. By switching off adiabatically the interactions, the trapped wave packets converge towards the true noninteracting bound states. Our numerical studies show how such scattering experiments can reveal and characte…
Strong coupling of molecules to the vacuum field of micro cavities can modify the potential energy surfaces opening new photophysical and photochemical reaction pathways. While the influence of laser fields is usually described in terms of classical field, coupling to the vacuum state of a cavity has to be described in terms of dressed photon-matter states (polaritons) which require quantized fields. We present a derivation of the non-adiabatic couplings for single molecules in the strong coupling regime suitable for the calculation of the dressed state dynamics. The formalism allows to use qu…
Stimulated Raman interaction of a classically pumped single three-level $Λ$-type atom in a resonator cavity featuring both radiative and unwanted losses is studied. It is shown that in the regime of stimulated adiabatic Raman passage the excited outgoing wave packet of the cavity-assisted electromagnetic field can be prepared in a one-photon Fock state with high efficiency. In this regime, the spatio-temporal shape of the wave packet does not depend on the interaction shape of the pump field, provided that the interaction of the atom with the pump is time-delayed with respect to the interactio…
We present a universal physical picture for describing storage and retrieval of photon wave packets in a Lambda-type atomic medium. This physical picture encompasses a variety of different approaches to pulse storage ranging from adiabatic reduction of the photon group velocity and pulse-propagation control via off-resonant Raman fields to photon-echo based techniques. Furthermore, we derive an optimal control strategy for storage and retrieval of a photon wave packet of any given shape. All these approaches, when optimized, yield identical maximum efficiencies, which only depend on the optica…
We report on the measurement of the time required for a wave packet to tunnel through the potential barriers of an optical lattice. The experiment is carried out by loading adiabatically a Bose-Einstein condensate into a 1D optical lattice. A sudden displacement of the lattice by a few tens of nm excites the micromotion of the dipole mode. We then directly observe in momentum space the splitting of the wave packet at the turning points and measure the delay between the reflected and the tunneled packets for various initial displacements. Using this atomic beam splitter twice, we realize a chai…
The decomposition of electronic and nuclear motion presented in~[A. Abedi, N. T. Maitra, and E. K. U. Gross, Phys. Rev. Lett. 105, 123002 (2010)] yields a time-dependent potential that drives the nuclear motion and fully accounts for the coupling to the electronic subsystem. Here we show that propagation of an ensemble of independent classical nuclear trajectories on this exact potential yields dynamics that are essentially indistinguishable from the exact quantum dynamics for a model non-adiabatic charge transfer problem. We point out the importance of step and bump features in the exact pote…
By using a wave packet approach, this paper reviews the Jaynes-Cummings model with and without the rotating wave approximation in a non-standard way. This gives new insight, not only of the two models themselves, but of the rotating wave approximation as well. Expressing the models by field quadrature operators, instead of the typically used boson ladder operators, wave packet simulations are presented. Several known phenomena of these systems, such as collapse-revivals, Rabi oscillation, squeezing and entanglement, are reviewed and explained in this new picture, either in an adiabatic or diab…
An ultracold wave packet of bosonic atoms loaded into a travelling laser wave may form a many-atom soliton.This is disturbed by a homogeneous force field, for example by the inevitable gravitation. The wave packet is accelerated and therefore the laser frequency appears to be chirped in the rest frame of the atoms. We derive the effective nonlinear Schrödinger equation. It shows a time dependent nonlinearity coefficient which amounts to a damping or antidamping, respectively. The accelerated packet solution remains a soliton which changes its shape adiabatically. Similarly, an active shaping c…
We use the dressed potentials obtained in the adiabatic representation of two coupled channels to calculate s-wave Feshbach resonances in a 3D spherically symmetric potential with an open channel interacting with a closed channel. Analytic expressions for the s-wave scattering length $a$ and number of resonances are obtained for a piecewise constant model with a piecewise constant interaction of the open and closed channels near the origin. We show analytically and numerically that, for strong enough coupling strength, Feshbach resonances can exist even when the closed channel does {\em not} h…
Following the Dirac-Frenkel time-dependent variational principle, transient dynamics of a one-dimensional Holstein polaron with diagonal and off-diagonal exciton-phonon coupling in an external electric field is studied by employing the multi-D$_2$ {\it Ansatz}, also known as a superposition of the usual Davydov D$_2$ trial states. Resultant polaron dynamics has significantly enhanced accuracy, and is in perfect agreement with that derived from the hierarchy equations of motion method. Starting from an initial broad wave packet, the exciton undergoes typical Bloch oscillations. Adding weak exci…
We consider the evolution of an initially localized wave packet after a sudden change in the Hamiltonian, i.e.\ a quench. When both bound and scattering eigenstates exist in the post-quench Hamiltonian, one might expect partial delocalization of the wave packet to ensue. Here we show that if the quench consists of a sudden switching-off of short-range inter-particle interactions, then Tan's universal relations guarantee delocalization through the high-momentum tail of the momentum distribution. Furthermore, we consider the influence of the range of the interaction and show how a finite range a…
The charge transfer in low energy (0.25 to 150 eV/amu) H($nl$) + He$^+(1s)$ collisions is investigated using a quasi-molecular approach for the $n=2,3$ as well as the first two $n=4$ singlet states. The diabatic potential energy curves of the HeH$^+$ molecular ion are obtained from the adiabatic potential energy curves and the non-adiabatic radial coupling matrix elements using a two-by-two diabatization method, and a time-dependent wave-packet approach is used to calculate the state-to-state cross sections. We find a strong dependence of the charge transfer cross section in the principal and …
