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arXiv:1512.01838 · Physical Review Letters

Observation of Quantum Interference between Separated Mechanical Oscillator Wave Packets

Daniel Kienzler, Christa Flühmann, Vlad Negnevitsky, Hsiang-Yu Lo, Matteo Marinelli, D. P. Nadlinger, Jonathan Home

Published Apr 5, 2016• 100 citations
arXivHTMLPDF

Abstract

We directly observe the quantum interference between two well-separated trapped-ion mechanical oscillator wave packets. The superposed state is created from a spin-motion entangled state using a heralded measurement. Wave packet interference is observed through the energy eigenstate populations. We reconstruct the Wigner function of these states by introducing probe Hamiltonians which measure Fock state populations in displaced and squeezed bases. Squeezed-basis measurements with 8 dB squeezing allow the measurement of interference for Δα=15.6, corresponding to a distance of 240 nm between the two superposed wave packets.

DOI
10.1103/physrevlett.116.140402

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We directly observe the quantum interference between two well-separated trapped-ion mechanical oscillator wave packets. The superposed state is created from a spin-motion entangled state using a heralded measurement. Wave packet interference is observed through the energy eigenstate populations. We reconstruct the Wigner function of these states by introducing probe Hamiltonians which measure Fock state populations in displaced and squeezed bases. Squeezed-basis measurements with 8 dB squeezing allow the measurement of interference for Δα=15.6, corresponding to a distance of 240 nm between the two superposed wave packets.
We observe the phase space trajectory of an entangled wave packet of a trapped ion with high precision. The application of a spin-dependent light force on a superposition of spin states allows for coherent splitting of the matter wave packet such that two distinct components in phase space emerge. We observe such motion with a precision of better than 9% of the wave packet extension in both momentum and position, corresponding to a 0.8 nm position resolution. We accurately study the effect of the initial ion temperature on the quantum entanglement dynamics. Furthermore, we map out the phonon distributions throughout the action of the displacement force. Our investigation shows corrections to simplified models of the system evolution. The precise knowledge of these dynamics may improve quantum gates for ion crystals and lead to entangled matter wave states with large displacements.
Classically, wave interference is a phenomenon that can be explained by considering only the waves themselves, that is, without the need to consider the apparatus that monitors or observes them. Thus, in classical theories, interference can only occur between waves of the same nature. In quantum theory, the observed results require a description of the system and its measuring apparatus, which allows us to rethink the explanation of various natural phenomena. In this paper, we consider the ion-trap platform to study the interference of waves with different physical natures, specifically the electromagnetic and mechanical. At first, we drive two lasers onto a single-trapped ion to produce Jaynes-Cummings and Carrier interactions, where we verify that, depending on the phase relationship between the coherent state of the vibrational (mechanical) mode and the Carrier pulse (electromagnetic wave), the interactions enhance or cancel out population transfer to the electronic state of the ion, that works out as our measuring apparatus for those waves. Extending our result to an ion chain, we verify that a precise modulation of the Carrier Rabi frequency and phase (electromagnetic pulse) according to the amplitude of the incoming mechanical coherent state in the ion chain enables creating either constructive or destructive interference with propagating pulses, in which the electronic state of the driven ion is, respectively, populated more and faster, or transparent to both pulse waves, when the information flux behaves as if no external fields are applied. Finally, this new type of controlled interference between waves of different natures allows us to propose new hybrid quantum devices, such as transistors or filters of wave packets, where photonic (phononic) pulses control the passage of phononic (photonic) waves.
For a single ion trapped in a harmonic potential under localization conditions beyond the Lamb-Dicke region, a motional wave packet can be coherently split by irradiating the trapped ion with appropriate counterpropagating traveling-wave laser pulses tuned to the second-sideband Raman resonance. Quantum interference between the split wave packets gives rise to interference fringes in the spatial probability distribution when the wave packets spatially overlap at a certain time during a periodic oscillation. An ion-trap interferometer is proposed on the basis of the wave-packet splitter in combination with quantum tomographic determination of the spatial interference fringes.
Detection of the weakest forces in nature is aided by increasingly sensitive measurements of the motion of mechanical oscillators. However, the attainable knowledge of an oscillator's motion is limited by quantum fluctuations that exist even if the oscillator is in its lowest possible energy state. We demonstrate a technique for amplifying coherent displacements of a mechanical oscillator with initial magnitudes well below these zero-point fluctuations. When applying two orthogonal squeezing interactions, one before and one after a small displacement, the displacement is amplified, ideally with no added quantum noise. We implemented this protocol with a trapped-ion mechanical oscillator and determined an increase by a factor of up to 7.3 (±0.3) in sensitivity to small displacements.
Full coherent control and generation of nonclassical superpositions of the quantum harmonic oscillator are not only of fundamental interest but are crucial for applications in quantum simulations, quantum-enhanced metrology, and continuous-variable quantum computation. Here, we create arbitrary superpositions of nonclassical and non-Gaussian states of a quantum harmonic oscillator using the motion of a trapped ion coupled to its internal spin states. We interleave spin-dependent nonlinear interactions with midcircuit spin measurements that herald the probabilistic preparation of superpositions of squeezed, trisqueezed, and quadsqueezed states, which have not previously been experimentally demonstrated. We achieve independent control over the complex-valued squeezing parameter and the probability amplitude of each constituent, as well as their spatial separation. We directly observe the nonclassical nature of these states in the form of Wigner negativity following a full-state reconstruction. Our methods apply to any system where a quantum harmonic oscillator is coupled to a spin.
The relation between quantum interference and classical interference is discussed in terms of the Wigner function and an analogous classical expression. For two displaced coherent states and two displaced electric-field Gaussian pulses, both the quantum-mechanical and classical Wigner functions exhibit oscillatory behavior. Classical analogs of squeezing, photon-number oscillation, and the QQQ function are presented.