Quantum Superposition of a Nanoparticle: Gluing It to a Single Electron
Context
Optical levitation of nanoparticles has already made it possible to cool their motion to the quantum ground state and to observe quantum effects, but preparing nonclassical states of the center of mass remains a hard problem. Standard schemes require nonlinear potentials, which, because of the diffraction limit, give spatial variations on the order of a micrometer, whereas the width of the particle's wavepacket in the ground state is about 10 picometers. So one usually resorts to expanding the wavepacket and then recapturing it, but a large spatial separation sharply accelerates decoherence. This work stands apart from that mainstream: instead of expanding the state, it exploits the quantum nature of a single electron, which acts as a microscopic "agent" influencing a mesoscopic object. Nearby in the archive there are papers on quantum networks as gravitational laboratories, on Schrödinger cats made of thousands of atoms, and on quantum algorithms, but there are almost no direct neighbors solving the same problem of gluing an electron to a nanoparticle.
Methods
The protocol begins by preparing a charged levitating nanoparticle (radius 50 nm, trap frequency 100 kHz) in the ground state of a harmonic trap. Then a single electron is prepared in a time-bin state: a superposition of early and late arrival times with a controllable phase. The electron collides with the particle's surface and sticks, reducing its charge by one elementary unit. At the same time, a short electric field pulse is applied, with a profile chosen so that if the electron arrived early, the particle receives a momentum kick in one direction, and if it arrived late, in the opposite direction. The field switches in a time much shorter than the particle's oscillation period, so during preparation its motion and decoherence are frozen. The particle then evolves in the harmonic trap for half a period, and its position is measured with a resolution of about 85 pm. By repeating the experiment at different phases of the electron state, the interference pattern is reconstructed.
Results
In the ideal case, after the collision and the field pulse, the particle ends up in a superposition of two coherent states with opposite momenta, that is, in a "Schrödinger kitten" state. At phase π, the Wigner function is negative at the origin of phase space, which is a signature of nonclassicality. For realistic parameters (momentum kick equal to the zero-point momentum p0, initial thermal occupation 0.5, decoherence rate Γ = 0.2ω), the interference visibility reaches 50%. When the kick is increased to 2p0, the visibility drops to 10%. Decoherence is mainly caused by photon recoil from the trap laser, but the negativity of the Wigner function persists for about 5π/12 of a period, and with a threefold reduction of decoherence, throughout the entire protocol. Cooling to the ground state is not critical: even with an average phonon number of about 1, the visibility remains high thanks to the small wavepacket size and the fast protocol time (half a period = 5 μs).
Implications
The work offers a fundamentally different route to macroscopic quantum superpositions than neighboring studies. Instead of expanding the wavepacket, using nonlinear potentials, or releasing and recapturing the particle, it uses direct transfer of quantum coherence from a single electron to a mesoscopic object. This is the first scheme in which phase control of a microscopic system (the electron) generates interference in the motion of an object that is $10^{12}$ times more massive. Such an approach removes the requirement for precision control over the nanoparticle itself, shifting the complexity onto the well-developed technique of electron interferometry. If the protocol is realized, it will make it possible to create quantum superpositions of objects at least five times more massive than the current record, opening experimental tests of collapse models and quantum gravity.
Future development
The immediate next step is to improve the interference visibility by reducing decoherence from photon recoil. Using radially polarized vector beams can cut the heating rate by a factor of three, which would preserve the negativity of the Wigner function throughout the entire protocol. Another direction is to increase the momentum kick to create more distinguishable states, although this enhances decoherence. It is also possible to optimize the electric field profile for particles with arbitrary initial charge, which has already been considered in the appendix. In the longer term, the protocol could be combined with methods of quantum control of motion to prepare more complex nonclassical states, such as superpositions of Fock states or squeezed states.
Impact
The method could be used in precision force metrology, since superpositions of momentum states increase sensitivity to external influences. It also provides a new tool for testing fundamental limits of quantum mechanics, including spontaneous collapse models and possible quantum gravity effects.
Next steps
Experimental implementation will require integrating a single-electron source with an optical trap and precisely synchronizing the electric pulse with the moment of collision. Then it will be necessary to demonstrate interference fringes and measure their visibility as a function of the electron state phase.
Key open problems
In levitated optomechanics, the key unsolved problem remains the creation and verification of macroscopic quantum superpositions at ever larger masses. This work attacks that problem directly, bypassing the main obstacle: rapid decoherence under spatial separation of wavepackets. It also links the task to single-electron physics, where coherence is well controlled, which may stimulate cross-disciplinary experiments.
A particle with a radius of 50 nanometers contains about $10^{10}$ atoms, and its mass exceeds the electron mass by a factor of $10^{12}$. Yet a single electron can put it into a quantum superposition of two different momenta. For comparison: it is as if a collision with a speck of dust made a soccer ball fly in two opposite directions at the same time.
The idea of a macroscopic quantum superposition echoes Schrödinger's thought experiment about a cat that is simultaneously alive and dead. In Ted Chiang's story "Story of Your Life" (and the film "Arrival"), the aliens perceive time nonlinearly, which resembles the time-bin state, where the electron is in a superposition of two arrival times.
Key numbers
- nanoparticle radius: 50 nm
- trap frequency: 100 kHz
- oscillation period: 10 μs
- momentum kick duration: 100 ns
- electric field strength: 360 V/m
- interference visibility: 50% at δp = p0
- particle mass relative to the electron: 1012