Quantum entanglement and modulation enhancement of free-electron-bound-electron interaction

Abstract

The modulation and engineering of the free-electron wave function bring new ingredient to the electron-matter interaction. We study the dynamics of a free-electron passing by a two-level system fully quantum mechanically and emphasize the enhancement of interaction from the modulation of the free-electron wave function. In presence of modulation of the free-electron wave function, we show that the electron energy loss/gain spectrum is greatly enhanced for a coherent initial state of the two-level system, which can function as a probe of the atomic coherence. We further find that distantly separated two-level atoms can be entangled through interacting with the same free electron. For a dilute beam of modulated electrons interacting with the atom, our theory shows the enhanced interaction due to resonant modulation.

Integrated photonics enables continuous-beam electron phase modulation

“…The corresponding modulation of the electronic wavefunction at optical frequencies is quantum-coherent in nature [15,19], and thus can be used for the coherent control of electron quantum states in space [16,18,50,51] and time [17,21,22]. Recent theoretical work suggest that such modulated electron beams enable an electron-mediated transfer of optical coherence, predicting the generation of coherent cathodoluminescence, the resonant excitation of two-level systems, and superradiance from sequential electrons [52][53][54][55]. These developments imply a future close integration of electron microscopy with coherent optical spectroscopy, with opportunities in local quantum control and enhanced sensing.…”

Tailored high-contrast attosecond electron pulses for coherent excitation and scattering

“…Besides their direct use for attosecond streaking and spectroscopy, such density-modulated electron beams are proposed for a multitude of applications, e.g., to imprint an external phase onto cathodoluminescence (CL) [38][39][40][41], to induce a microscopic polarization in two-level systems (TLS), or to coherently build up mode amplitudes or local polarizations using independent electrons [42][43][44][45][46][47], thus promising a merger of electron microscopy with coherent spectroscopy.…”

“…A key limitation for these efforts is the quality of compression and the amount of uncompressed background density [34,36,37,45,48], sometimes described by the classical multi-electron bunching factor for SASE-FELs [49][50][51][52]. However, even for a pure single-electron state [53][54][55] focused in the quantum regime [34], limited coherence arises [39,[41][42][43]46].…”

“…Applications of background-free pulses.-We note that the background-free attosecond pulses produced by this scheme will be exceedingly useful in a number of recently proposed schemes for coherent interactions of free electrons with nanostructures and quantum systems. This includes electron-mediated coherence transfer and the coherent build-up of excitations for multiple subsequent electrons [38,39,[41][42][43][44][45][46][47]. In each of the underlying processes, the modulation amplitude of the electron density at the fundamental modulation frequency, or its harmonics, plays a major role.…”

“…In each of the underlying processes, the modulation amplitude of the electron density at the fundamental modulation frequency, or its harmonics, plays a major role. This is quantified by the expectation values or moments b n of the ladder operator b = exp(iωt) [43,67]. Different terminologies relating to these expectation values have been used, including the degree of coherence [39], the coherence factor [68], or the bunching factor [38,51,52,69].…”