Spin–motion entanglement and state diagnosis with squeezed oscillator wavepackets

Abstract

Mesoscopic superpositions of distinguishable coherent states provide an analog to the Schrödinger's cat thought experiment [1,2]. For mechanical oscillators these have primarily been realised using coherent wavepackets, for which the distinguishability arises due to the spatial separation of the superposed states [3][4][5]. Here, we demonstrate superpositions composed of squeezed wavepackets, which we generate by applying an internal-state dependent force to a single trapped ion initialized in a squeezed vacuum state with 9 dB reduction in the quadrature variance. This allows us to characterise the initial squeezed wavepacket by monitoring the onset of spin-motion entanglement, and to verify the evolution of the number states of the oscillator as a function of the duration of the force. In both cases, we observe clear differences between displacements aligned with the squeezed and anti-squeezed axes. We observe coherent revivals when inverting the state-dependent force after separating the wavepackets by more than 19 times the ground state root-mean-square extent, which corresponds to 56 times the r.m.s. extent of the squeezed wavepacket along the displacement direction. Aside from their fundamental nature, these states may be useful for quantum metrology [6] or quantum information processing with continuous variables [7][8][9].The creation and study of nonclassical states of spin systems coupled to a harmonic oscillator has provided fundamental insights into the nature of decoherence and the quantum-classical transition. These states and their control form the basis of experimental developments in quantum information processing and quantum metrology [1,2,10]. Two of the most commonly considered states of the oscillator are squeezed states and superpositions of coherent states of opposite phase, which are commonly referred to as "Schrödinger's cat" (SC) states. Squeezed states involve reduction of the fluctuations in one quadrature of the oscillator below the ground state uncertainty, which has been used to increase sensitivity in interferometers [11,12]. SC states provide a complementary sensitivity to environmental influences by separating the two parts of the state by a large distance in phase space. These states have been created in microwave and optical * Electronic address:hylo@phys.ethz.ch; Electronic address: jhome@phys.ethz.ch cavities [2,13], where they are typically not entangled with another system, and also with trapped ions [1,[3][4][5], where all experiments performed have involved entanglement between the oscillator state and the internal electronic states of the ion. SC states have recently been used as sensitive detectors for photon scattering recoil events at the single photon level [14].In this Letter, we use State-Dependent Forces (SDFs) to create superpositions of distinct squeezed oscillator wavepackets which are entangled with a pseudo-spin encoded in the electronic states of a single trapped ion. We will refer to these states as Squeezed Wavepacket Entangled States (SWES) in the rest of ...

Quantum Simulation of the Quantum Rabi Model in a Trapped Ion

“…Therefore, we expect to observe quantum dynamics due to the strong-coupling effect. We note that the degenerate case has been investigated thoroughly for the production of Schrödinger's cat states [31][32][33][34][35][36] and the calibration of two-qubit Mølmer-Sørensen gates [37][38][39][40][41][42] in trapped-ion systems. Although the spin-dependent force is a welldeveloped technique for the trapped-ion community, it has never been viewed as the simulation of a special case of the QRM.…”

“…2 and 3, we obtain the phonon-number distribution. This is performed by driving a resonant bluesideband transition j↓; ni ↔ j↑; n þ 1i followed by a spin projective measurement and fitting the obtained spinexcitation evolution with the formula [11,29,35] P j↑i ðtÞ ¼ 1 2…”

Optimized tomography of continuous variable systems using excitation counting

“…There have been significant advances in excitation counting over various physical platforms, including optical photons [21], microwave photons [22][23][24][25], and phonons of trapped ions [26][27][28]. In particular, the capability of quantum non-demolition measurement of microwave excitation number has been demonstrated with superconducting circuits [29].…”

“…For example, up to a displacement, the Husimi Q function can be regarded as the probability of zero excitation, and the Wigner function can be obtained from the difference between probabilities associated with even and odd number of excitations. We expect more cost-effective QST by collecting full population distributions upon various displacements using excitation counting, which can be efficiently achieved in various CV systems [21][22][23][24][25][26][27][28][29].…”

Spatial compression of a particle state in a parabolic potential by spin measurements

“…Production of coherent state of an ion in a parabolic potential has also been shown to be feasible in an ion trap 12 . Due to the high interest in circuit quantum electrodynamics and ion trap experiments, spatially localized states are important for the particle manipulation (see for example [13][14][15] ). A widely used approach to generate and control the quantum state of a target system is by designing a set of tailored selective (where the outcome is either discarded or accepted, dependent on the measurement result) measurements of an ancilla coupled to the target.…”