Quantum Memory from Quantum Dynamics

Ideas from quantum optics based on coherence and interference have proven extremely successful for the study and manipulation of atoms and molecules. Recent improvements in existing and upcoming x-ray light sources prompt the question, whether such techniques could also be applied in the hard x-ray regime. This would not only be essential for fully exploiting the potential of the new machines, but also could pave the way for new applications. In turn, x-ray quantum optics could also evolve into a promising new platform for the study of light-matter interactions. In this talk, I will review our recent theoretical and experimental progress in developing quantum optics with hard x-rays. A particular focus will be placed on experiments involving the measurement and control of the x-ray phase, which is an important challenge in x-ray science.

The non-Markovianity of a quantum process $\Lambda_t$ may be defined in terms of either (i) contractivity or (ii) positivity of the intermediate quantum maps. More precisely, as shown by Chruscinski, Kossakowski and Rivas [PRA (2011)], contractivity is equivalent to positivity and contractivity of the dilated process ${\rm Id}\otimes\Lambda_t$ is equivalent to complete positivity. It is thought that complete positivity is the easiest criteria to check, as it just requires to diagonalize the eigenvalues of the Choi-matrix representation of the intermediate quantum maps. In this work, we describe a method which allows to check contractivity in a fully analytical manner.

Recollision for a laser driven atomic system is investigated in the relativistic regime. We find the relativistic recollision energy cutoff is independent of the ponderomotive potential Up, in contrast to the well-known 3.2Up scaling, and determined by the ionization potential of the atomic system. The ultimate energy cutoff is limited by the available intensities of short wavelength lasers and cannot exceed a few thousand Hartree, setting a boundary for recollision based attosecond physics.

The interaction of atomic systems with laser fields in the regime, where the typical time of the laser field oscillation is large compared with the orbit time of the bound system, is investigated. When additionally the field is weak compared with the atomic field strength the ionization happens via multiphoton ionization, for intermediate field strength tunnel ionization dominates and for strong fields over-the-barrier ionization is the physical process. All three processes have clear intuitive physical pictures. In this talk we will try to shed some light on the ionization process happening at parameters that are in the transition region of the three described processes, by presenting calculations of ionization probabilities and electron trajectories via a strong-field approximation and a perturbation theory in the laser field strength.

The interaction of gapped graphene (a class of materials similar or based on graphene) with strong fields is studied in the two-band approximation. First, we study the transition from perturbative to fully nonperturbative regime of HHG. Next, the signatures of Floquet-Bloch states in the low-order harmonic spectra are studied. We find field-strength-dependent shifts of the position of resonant peaks in the low-order harmonic spectra. These shifts are analogous to the ponderomotive shifts in the strong field physics.

In molecular dynamics calculations, the Pauli principle is frequently enforced by complex Pauli potentials that tend to keep the phase space distance of two fermionic particles large. We show by a semiclassical simulation of a scattering process between two electrons that no such potential is needed if the dynamics is started from a suitably symmetrized initial state and is described by the Herman-Kluk propagator [1]. [1] F. Grossmann, M. Buchholz, E. Pollak, and M. Nest, Phys. Rev. A 89, 032104 (2014)

Presenting true crossings of adiabatic potential energy surfaces, conical intersections are a paradigm of ultrafast and efficient electronic relaxation dynamics. The same mechanism is shown to apply also for vibrational conical intersections, which may occur when two high-frequency modes (such as OH stretch vibrations) are coupled to low-frequency modes (such as hydrogen bonding modes). By derivation of a model Hamiltonian and its parametrization for a concrete example, the hydrogen-bonded complex HCO−2 · H2O, the conditions that such conical intersections occur are identified and the consequences for the vibrational dynamics and spectra are demonstrated.

The struggle with correlated particles that started 20 years ago continues until today. Basic understanding gained and critical thinking learned in early years spreads out now to more and more undefined stuff.

I discuss the appearance of memory terms in open quantum system dynamics and its relation to notions of Markovian vs. non-Markovian evolution. A stochastic version of the traditional Nakajima-Zwanzig approach is presented.

We argue that the alignment of Lyapunov vectors provides a quantitative criterion to predict the imminence of large-amplitude events in chaotic time-series of observables generated by sets of ordinary differential equations. Explicit predictions are reported for a Rössler oscillator and for a semiconductor laser with optoelectronic feedback.

We investigate the coupled electron-nuclear dynamics in model systems showing avoided crossings [1] and conical intersections [2], respectively. It is demonstrated that the nuclear density conserves its initial Gaussian shape when passing the nuclear configurations where strong non-adiabatic couplings exist. This is in sharp contrast to the picture which evolves from an analysis within the basis of adiabatic electronic states. There, dramatic changes are seen in the dynamics of the different nuclear components of the total wave function. It is thus documented that, in the case of a highly efficient population transfer between the respective adiabatic states, neither the nuclear nor the electronic density are influenced by the existence of the crossing or conical intersection. This is the case because the nuclear-electronic wave packet moves on a potential energy surface which changes its topology smoothly as a function of all particle coordinates. [1] J. Albert, D. Kaiser, V. Engel, J. Chem. Phys. 144, 171103 (2016) [2] K. Hader, J. Albert, E.K.U. Gross, V. Engel, J. Chem. Phys. 146, 074304 (2017)

Numerical simulations and analytical results on the creation of excitons and bi-excitons by short, strong laser pulses are presented. In particular, the interplay between strong external driving and dissipative effects due to the substrate phonons is analyzed. One of the main experimental findings is a driving-dependent relaxation mechanism, which manifests itself both in the regime of Rabi oscillations as well as for adiabatic passage using chirped pulses. The experiments are well reproduced by numerical simulations based on a Non-Markovian master equation approach, and the exciton dynamics for different pulses is analyzed in terms of its “non-Markovian” or “Markovian” character. Finally, an analytical model is constructed, which captures all of the experimental findings, and which allows to identify different dynamical regimes in terms of the quantum dot characteristics and laser parameters. On the basis of this model, clear indications on robust exciton and bi-exciton generation can be given, which are confirmed by recent experiments.

It's been a while since we last heard from progress in the few-body problem. I will try to report on some efforts to break or justify this silence.

Echo phenomena are playing an important role, both in classical and quantum physics: Prominent examples are reunions on the classical side and spin echoes on the quantum side. However, the latter represent rather specific quantum systems living in a low-dimensional Hilbert space and involving only discrete degrees of freedom. Is it possible to generalize this concept to systems with continuous degrees of freedom governed by Theoretical Quantum Dynamics?

Clusters are a form of matter in between atoms and the condensed phase. I will describe how the respond to short intense light pulses of different frequencies by ejecting electrons. Despite the many-body character, the highest photo electron energy follows from a simple description with recollision features of strong field dynamics. As a result clustering phenomena of Freiburg’s Quantum Dynamics can be put into perspective…

Attosecond time-resolved spectroscopy is a thought-provoking method for investigating the electronic dynamics in atoms [1], and this technique is now being transferred to the scrutiny of electronic excitations, electron propagation, and collective electronic (plasmonic) effects in solid surfaces [1,2,3] and nanoparticles [1,4,5]. Compared with photoemission from isolated gaseous atoms, numerical simulations of such experiments on complex targets require, in addition, the adequate modeling of (i) the target’s electronic band structure [2], (ii) elastic and inelastic scattering of released photoelectrons inside the solid [2-5], (iii) surface and bulk collective electronic excitations [1,4,5], (iv) the screening and reflection of the assisting IR-laser field at the solid surface [3], (v) the influence of equilibrating residual charge distributions on emitted photoelectrons, and (vi) the effect of spatially inhomogeneous plasmonic fields on the photoemission process [2,4]. This talk will review the extent to which photoelectron propagation in matter and the plasmonic response of nanostructures can be (a) represented in classical [1,5] and quantum mechanical [1-4] simulations and (b) retrieved in IR-streaked XUV [1,2,4,5] and IR-XUV two-photon interference (RABBITT) [3] photoemission spectra. As examples, I will discuss our recent numerical results for photoemission from (adsorbate-covered) metal surfaces [2,3] (in comparison with experimental data) and from plasmonic 10 to 200 nm diameter spherical nanoparticles that show how spatio-temporal information of the sub-infrared-cycle plasmonic and electronic dynamics is embedded in time-resolved spectra [4,5]. [1] U. T., Q. Liao, E. M. Bothschafter, F. Süßmann, M. F. Kling, R. Kienberger, in: Handbook of Photonics, Vol. 1, (Wiley 2015). [2] Q. Liao, U. T., Phys. Rev. A 89, 033849 (2014); ibid. 92, 031401(R) (2015). [3] M. J. Ambrosio, U. T., Phys. Rev. A 94, 063424 (2016). [4] J. Li, E. Saydanzad, U. T., Phys. Rev. A 94, 051401(R) (2016). [5] E. Saydanzad, J. Li, U. T., Phys. Rev. A, just submitted. Supported in part by the US NSF and DoE.

C. Basler and H. Helm Department of Molecular and Optical Physics Freiburg University In the presence of two-photon resonant laser fields superpositions of hyperfine Zeeman levels of rubidium reveal electromagnetically-induced transparency. Transparency appears when the relative phase of the two atomic states matches the local phase difference of the two laser fields. This feature is readily detected by monitoring the absorbance of Rb vapour(1). In the absence of decoherence superposition states memorize the quantum phase under which they were created - even when shielded from the laser fields. Pertinent to this is the match between the temporal development of the dynamic phase of the superposition and the phase of the resonant lasers. Thus transparency persists after the sample was blocked from the fields for some time and then illuminated again. This permits the exploration of geometric phases which can be imprinted in superposition states during “laser-off” time. We discuss experiments on magnitude and sign of geometric phases under adiabatic(2) and under nonadiabatic(3) quantum transport in time-varying magnetic fields. (1) C. Basler at al. Phys. Rev. A 87, 013430 (2013). (2) S. Welte, C. Basler and H. Helm, Phys. Rev. A 89, 023412 (2014). (3) C. Basler, H, Helm, H. P. Breuer, to be published.

The results of physical investigations both experimental and theoretical are communicated in many different ways, ranging from tables, mathematical formulae and fits, simple plots to quite complex graphical representations. Ideally the representations chosen should help to understand the results and motivate further research, but do we always succeed? I will discuss several sometimes surprising examples from our research, from angular distributions to features of Rydberg states.

The precise connection between quantum wave functions and the underlying classical trajectories often is presented rather vaguely by practitioners of quantum mechanics. Here we demonstrate, with simple examples, that the imaging theorem (IT) based on the semiclassical propagator provides a precise connection. Wave functions are preserved out to macroscopic distances but the variables, position and momentum, of these functions describe classical trajectories. We show that the IT, based on an overtly time-dependent picture, provides a strategy alternative to standard scattering theory with which to compare experimental results to theory.