Quantum coherent optical phase modulation in an ultrafast transmission electron microscope

Abstract

Coherent manipulation of quantum systems with light is expected to be a cornerstone of future information and communication technology, including quantum computation and cryptography. The transfer of an optical phase onto a quantum wavefunction is a defining aspect of coherent interactions and forms the basis of quantum state preparation, synchronization and metrology. Light-phase-modulated electron states near atoms and molecules are essential for the techniques of attosecond science, including the generation of extreme-ultraviolet pulses and orbital tomography. In contrast, the quantum-coherent phase-modulation of energetic free-electron beams has not been demonstrated, although it promises direct access to ultrafast imaging and spectroscopy with tailored electron pulses on the attosecond scale. Here we demonstrate the coherent quantum state manipulation of free-electron populations in an electron microscope beam. We employ the interaction of ultrashort electron pulses with optical near-fields to induce Rabi oscillations in the populations of electron momentum states, observed as a function of the optical driving field. Excellent agreement with the scaling of an equal-Rabi multilevel quantum ladder is obtained, representing the observation of a light-driven 'quantum walk' coherently reshaping electron density in momentum space. We note that, after the interaction, the optically generated superposition of momentum states evolves into a train of attosecond electron pulses. Our results reveal the potential of quantum control for the precision structuring of electron densities, with possible applications ranging from ultrafast electron spectroscopy and microscopy to accelerator science and free-electron lasers.

Attosecond electron pulse trains and quantum state reconstruction in ultrafast transmission electron microscopy

“…The temporal structuring of electron probe beams is facilitated by time-dependent fields in the radio-frequency [22][23][24] , terahertz 18,25 or optical domains. Promising a further leap in temporal resolution, recent findings suggest that ultrafast electron diffraction and microscopy with optically phasecontrolled and sub-cycle, attosecond-structured wave functions may be feasible 8,[26][27][28][29][30] . Specifically, light-field control may translate the temporal resolution of ultrafast transmission electron microscopy (UTEM) 31,32 and electron diffraction (UED) 10,33 , currently at about 200 fs 34 and 20 fs 14,23 , respectively, to the range of attoseconds 26,27,35 .…”

“…Equivalently, the quantum state can be written as a coherent superposition of momentum sidebands 26,29,30 . The action of two fields at frequencies ω and 2ω is now described in terms of two superimposed phase modulations, which for the typically small total energy changes (relative to the initial electron energy) results in the electron quantum state…”

“…For interaction with a single light field at frequency ω, the spatial wavefunction of the free-electron quantum state | ⟩ experiences a sinusoidal phase modulation in the beam direction 26,30 ,…”

Ultrafast nanoscale magnetic switching via intense picosecond electron bunches

“…Novel electron optical concepts promise a tremendous increase in temporal and spatial resolution allowing researchers to address new scientific challenges [2][3][4][5][6]. The use of relativistic MeV electron energies is an attractive avenue to deal with the issue of Coulomb repulsion in ultrashort electron pulses bringing single-shot electron microscopy on nm length-and ps time-scales within reach [7,8].…”

Quantum Control of Population Transfer and Vibrational States via Chirped Pulses in Four Level Density Matrix Equations

“…A central aspect in both approaches, CC and QCS, is the control of population transfer between the ground and excited states, as well as the generation of vibrational coherence in both potential surfaces. By controlling the population transfer or by suppressing specific molecular vibrational coherences, a photochemical reaction channel can be selectively chosen [27,29,32,[37][38][39][40][41][42][43][44][45][46][47][48][49], or a certain mode in a multidimensional time-resolved signal can be suppressed [37,[50][51][52][53][54][55].…”