We propose a scheme for generating high-mass quantum superposition states of an optically precooled, levitated nanoparticle through electron diffraction at its subnanometer crystal lattice. When a single electron undergoes Bragg diffraction at a free-falling nanoparticle, momentum conservation implies that the superposition of Bragg momenta is imprinted onto the relative coordinate between electron and nanoparticle, which entangles their wave functions. By imaging the electron interferogram, one maps the nanoparticle state onto a superposition of Bragg momenta, as if it was diffracted by its own lattice. This results in a coherent momentum splitting approximately 1000 times greater than what is achievable with two-photon recoils in conventional standing-wave gratings. Self-interference of the nanoparticle can thus be observed within drastically shorter free-fall times in a time-domain Talbot interferometer configuration, significantly relaxing source requirements and alleviating decoherence from environmental factors such as residual gas and thermal radiation. Shorter interference times also allow for a recapture of the nanoparticle within its initial trapping volume, facilitating its reuse in many rapid experimental duty cycles. This opens new possibilities for experimental tests of macroscopic quantum effects within a transmission electron microscope.
We propose a scheme for generating high-mass quantum superposition states of an optically precooled, levitated nanoparticle through electron diffraction at its subnanometer crystal lattice. When a single electron undergoes Bragg diffraction at a free-falling nanoparticle, momentum conservation implies that the superposition of Bragg momenta is imprinted onto the relative coordinate between electron and nanoparticle, which entangles their wave functions. By imaging the electron interferogram, one maps the nanoparticle state onto a superposition of Bragg momenta, as if it was diffracted by its own lattice. This results in a coherent momentum splitting approximately 1000 times greater than what is achievable with two-photon recoils in conventional standing-wave gratings. Self-interference of the nanoparticle can thus be observed within drastically shorter free-fall times in a time-domain Talbot interferometer configuration, significantly relaxing source requirements and alleviating decoherence from environmental factors such as residual gas and thermal radiation. Shorter interference times also allow for a recapture of the nanoparticle within its initial trapping volume, facilitating its reuse in many rapid experimental duty cycles. This opens new possibilities for experimental tests of macroscopic quantum effects within a transmission electron microscope.
Matter-wave interferometry is a phenomenon which has been utilized and studied in electron microscopy since the early days of electron optics, with the development of phase contrast imaging, electron diffraction, electron holography, etc. When an electron diffracts off of a crystal lattice, it enters a superposition state of eligible Bragg diffraction components; due to momentum conservation, the crystalline sample must receive an equal and opposite superposition of momentum transfers. In theory, this results in an entangled electron-sample state. Typically, however, the sample is extremely large relative to the electron and is held fast in a sample holder, and this reciprocal momentum transfer is unobservable [1]. We present a proposal [2] to establish a system where such momentum kicks would be resolvable, to enable probing of the matter-wave properties of the sample as well as the free electron. A crystalline silicon nanoparticle is levitated in the sample plane, then released from its trap to enter free-fall. A single electron impacts the nanoparticle and undergoes Bragg diffraction. The nanoparticle receives a momentum transfer from the diffraction and is allowed to continue free-falling for a fixed amount of time before recapture and measurement of its position, X. In synchrony, the position of the electron, x, is measured. Assuming perfect measurement resolution, we calculate the resulting interference pattern for a quantum interaction, where the nanoparticle can behave as a quantum wave (Fig. 1a), or for the case where it behaves as a classical grating aperture (Fig. 1b) for different recapture times, t. The quantum scenario presents additional fringes visible at specific recapture times. Such an experiment provides a test of the matter-wave behaviour of high mass nanoparticles, with an efficient duty cycle and a short interference time, and would allow access to electron-sample entanglement in a transmission electron microscope.
We propose a protocol for preparing mechanical Schrödinger kittens -- mesoscopic quantum superpositions of coherent motional states of an optically levitated nanoparticle -- by adhering single electron time-bin states to its surface. Over short protocol timescales, coherence of the mesoscopic superposition survives the dominant decoherence mechanisms afflicting levitated systems, and can be observed by varying the phase of the time-bin electrons. Interference fringes can be detected with real-time, near-Heisenberg limited interferometry of photons scattered from the particle. This approach eliminates the need for coherent state expansion, dark potentials, and particle release-and-recapture mechanisms, providing a new route to test quantum mechanics in unprecedented scales.
We perform free-fall experiments with a charge-neutral, optically levitated nanoparticle. This is achieved using an optical tweezer that can be rapidly toggled on and off and vertically displaced, enabling the particle to be released and recaptured after each free fall. The particle is insensitive to electric fields due to its charge neutrality and, during free evolution, is not subject to photon recoil heating. We achieve free-fall durations of up to 0.25 ms and observe a nearly two hundred-fold increase in the particle's position uncertainty at recapture. The current limit on the free-fall time arises from the performance of the initial cooling step. By implementing linear feedback techniques and reducing the background pressure, we expect to perform millisecond-scale free-fall experiments in ultra-high vacuum, opening new opportunities for generating large delocalizations of levitated objects.
We perform free-fall experiments with a charge-neutral, optically levitated nanoparticle. This is achieved using an optical tweezer that can be rapidly toggled on and off and vertically displaced, enabling the particle to be released and recaptured after each free fall. The particle is insensitive to electric fields due to its charge neutrality and, during free evolution, is not subject to photon recoil heating. We achieve free-fall durations of up to 0.25 ms and observe a nearly two hundred-fold increase in the particle's position uncertainty at recapture. The current limit on the free-fall time arises from the performance of the initial cooling step. By implementing linear feedback techniques and reducing the background pressure, we expect to perform millisecond-scale free-fall experiments in ultra-high vacuum, opening new opportunities for generating large delocalizations of levitated objects.
We perform free-fall experiments with a charge-neutral, optically levitated nanoparticle. This is achieved using an optical tweezer that can be rapidly toggled on and off and vertically displaced, enabling the particle to be released and recaptured after each free fall. The particle is insensitive to electric fields due to its charge neutrality, and during free evolution, is not subject to photon recoil heating. We achieve free-fall durations of up to 0.25ms and observe a nearly 200-fold increase in the particle's position uncertainty at recapture. The current limit on the free-fall time arises from the performance of the initial cooling step. By implementing linear feedback techniques and reducing the background pressure, we expect to perform millisecond-scale free-fall experiments in an ultrahigh vacuum, opening new opportunities for generating large delocalizations of levitated objects.
Levitated nanoparticles are a forerunner as an experimental platform to test the limits of quantum mechanics at a macroscopic scale. Some important initial steps have been made towards preparing a macroscopic quantum state of a relatively massive (femtogram) particle. Specifically, the community has achieved ground-state cooling of the center-of-mass motion of a nanoparticle levitated in an optical trap. One crucial further step is now to expand the wavefunction of the particle. This step should happen in the presence of a minimum of decoherence, which makes evolution in an optical trap (inevitably exerting measurement backaction) unsuitable.