Probing macroscopic realism via Ramsey correlation measurements

Degeneracy and Photon Trapping in a Dissipationless Two-Mode Optomechanical Model

In this work, we theoretically study a finite and undamped two-mode optomechanical model consisting of a high quality optical cavity containing a thin, elastic, and dielectric membrane. The main objective is to investigate the precursors of quantum phase transition in such a model by studying the behavior of some observables in the ground state. By controlling the coupling between membrane and modes, we find that the two lowest energy eigenstates become degenerate, as is indicated by the behavior of the mean value of some operators and by other quantifiers as a function of the coupling. Such degenerate states are characterized by a coherent superposition of eigenstates describing one of the two modes preferentially populated and the membrane dislocated from its equilibrium position due the radiation pressure (Schrödinger's cat states). The delocalization of the compound system photons+membrane results in an increase in fluctuations as measured by Robertson-Schrödinger uncertainty relations.

Weak versus Deterministic Macroscopic Realism, and Einstein-Podolsky-Rosen's Elements of Reality

The violation of a Leggett-Garg inequality confirms the incompatibility between quantum mechanics and the combined premises (called macro-realism) of macroscopic realism (MR) and noninvasive measurability (NIM). Arguments can be given that the incompatibility arises because MR fails for systems in a superposition of macroscopically distinct states-or else, that NIM fails. In this paper, we consider a strong negation of macro-realism, involving superpositions of coherent states, where the NIM premise is replaced by Bell's locality premise. We follow recent work and propose the validity of a subset of Einstein-Podolsky-Rosen (EPR) and Leggett-Garg premises, referred to as weak macroscopic realism (wMR). In finding consistency with wMR, we identify that the Leggett-Garg inequalities are violated because of failure of both MR and NIM, but also that both are valid in a weaker (less restrictive) sense. Weak MR is distinguished from deterministic macroscopic realism (dMR) by recognizing that a measurement involves a reversible unitary interaction that establishes the measurement setting. Weak MR posits that a predetermined value for the outcome of a measurement can be attributed to the system after the interaction, when the measurement setting is experimentally specified. An extended definition of wMR considers the "element of reality" defined by EPR for system A, where one can predict with certainty the outcome of a measurement on A by performing a measurement on system B. Weak MR posits that this element of reality exists once the unitary interaction determining the measurement setting at B has occurred. We demonstrate compatibility of systems violating Leggett-Garg inequalities with wMR but point out that dMR has been shown to be falsifiable. Other tests of wMR are proposed, the predictions of wMR agreeing with quantum mechanics. Finally, we compare wMR with macro-realism models discussed elsewhere. An argument in favour of wMR is presented: wMR resolves a potential contradiction pointed out by Leggett and Garg between failure of macro-realism and assumptions intrinsic to quantum measurement theory.

Analog Quantum Control of Magnonic Cat States on a Chip by a Superconducting Qubit

We propose to directly and quantum-coherently couple a superconducting transmon qubit to magnons-the quanta of the collective spin excitations, in a nearby magnetic particle. The magnet's stray field couples to the qubit via a superconducting quantum interference device. We predict a resonant magnon-qubit exchange and a nonlinear radiation-pressure interaction that are both stronger than dissipation rates and tunable by an external flux bias. We additionally demonstrate a quantum control scheme that generates magnon-qubit entanglement and magnonic Schrödinger cat states with high fidelity.

Direct Characteristic-Function Tomography of Quantum States of the Trapped-Ion Motional Oscillator

We implement direct readout of the symmetric characteristic function of quantum states of the motional oscillation of a trapped calcium ion. Suitably chosen internal state rotations combined with internal state-dependent displacements, based on bichromatic laser fields, map the expectation value of the real or imaginary part of the displacement operator to the internal states, which are subsequently read out. Combining these results provides full information about the symmetric characteristic function. We characterize the technique by applying it to a range of archetypal quantum oscillator states, including displaced and squeezed Gaussian states as well as two and three component superpositions of displaced squeezed states. For each, we discuss relevant features of the characteristic function and Wigner phase-space quasiprobability distribution. The direct reconstruction of these highly nonclassical oscillator states using a reduced number of measurements is an essential tool for understanding and optimizing the control of oscillator systems for quantum sensing and quantum information applications.

Pulsed Quantum-State Reconstruction of Dark Systems

We propose a novel strategy to reconstruct the quantum state of dark systems, i.e., degrees of freedom that are not directly accessible for measurement or control. Our scheme relies on the quantum control of a two-level probe that exerts a state-dependent potential on the dark system. Using a sequence of control pulses applied to the probe makes it possible to tailor the information one can obtain and, for example, allows us to reconstruct the density operator of a dark spin as well as the Wigner characteristic function of a harmonic oscillator. Because of the symmetry of the applied pulse sequence, this scheme is robust against slow noise on the probe. The proof-of-principle experiments are readily feasible in solid-state spins and trapped ions.

Painting Nonclassical States of Spin or Motion with Shaped Single Photons

We propose a robust scheme for generating macroscopic superposition states of spin or motion with the aid of a single photon. Shaping the wave packet of the photon enables high-fidelity preparation of nonclassical states of matter even in the presence of photon loss. Success is heralded by photodetection, enabling the scheme to be implemented with a weak coherent field. We analyze applications to preparing Schrödinger cat states of a collective atomic spin or of a mechanical oscillator coupled to an optical resonator. The method generalizes to preparing arbitrary superpositions of coherent states, enabling full quantum control. We illustrate this versatility by showing how to prepare Dicke or Fock states, as well as superpositions in the Dicke or Fock basis.

Nonclassicality of the Harmonic-Oscillator Coherent State Persisting up to the Macroscopic Domain

Can the most "classical-like" of all quantum states, namely the Schrödinger coherent state of a harmonic oscillator, exhibit nonclassical behavior? We find that for an oscillating object initially in a coherent state, merely by observing at various instants which spatial region the object is in, the Leggett-Garg inequality (LGI) can be violated through a genuine negative result measurement, thereby repudiating the everyday notion of macrorealism. This violation thus reveals an unnoticed nonclassicality of the very state which epitomizes classicality within the quantum description. It is found that for any given mass and oscillator frequency, a significant quantum violation of LGI can be obtained by suitably choosing the initial peak momentum of the coherent state wave packet. It thus opens up potentially the simplest way (without coupling with any ancillary quantum system or using nonlinearity) for testing whether various recently engineered and sought after macroscopic oscillators, such as feedback cooled thermal trapped nanocrystals of ∼10^{6}-10^{9}  amu mass, are indeed bona fide nonclassical objects.

Enhanced violations of Leggett-Garg inequalities in an experimental three-level system

Leggett-Garg inequalities are tests of macroscopic realism that can be violated by quantum mechanics. In this letter, we realise photonic Leggett-Garg tests on a three-level system and implement measurements that admit three distinct measurement outcomes, rather than the usual two. In this way we obtain violations of three- and four-time Leggett-Garg inequalities that are significantly in excess of those obtainable in standard Leggett-Garg tests. We also report violations the quantum-witness equality up to the maximum permitted for a three-outcome measurement. Our results highlight differences between spatial and temporal correlations in quantum mechanics.

Pulsed Entanglement of Two Optomechanical Oscillators and Furry's Hypothesis

A strategy for generating entanglement between two separated optomechanical oscillators is analyzed, using entangled radiation produced from down-conversion and stored in an initiating cavity. We show that the use of pulsed entanglement with optimally shaped temporal modes can efficiently transfer quantum entanglement into a mechanical mode, then remove it after a fixed waiting time for measurement. This protocol could provide new avenues for testing for bounds on decoherence in massive systems that are spatially separated, as originally suggested by Furry not long after the discussion by Einstein-Podolsky-Rosen and Schrödinger of entanglement.

Measurements of nanoresonator-qubit interactions in a hybrid quantum electromechanical system

Experiments to probe the basic quantum properties of motional degrees of freedom of mechanical systems have developed rapidly over the last decade. One promising approach is to use hybrid electromechanical systems incorporating superconducting qubits and microwave circuitry. However, a critical challenge facing the development of these systems is to achieve strong coupling between mechanics and qubits while simultaneously reducing coupling of both the qubit and mechanical mode to the environment. Here we report measurements of a qubit-coupled mechanical resonator system consisting of an ultra-high-frequency nanoresonator and a long coherence-time superconducting transmon qubit, embedded in a superconducting coplanar waveguide cavity. It is demonstrated that the nanoresonator and transmon have commensurate energies and transmon coherence times are one order of magnitude larger than for all previously reported qubit-coupled nanoresonators. Moreover, we show that numerical simulations of this new hybrid quantum system are in good agreement with spectroscopic measurements and suggest that the nanoresonator in our device resides at low thermal occupation number, near its ground state, acting as a dissipative bath seen by the qubit. We also outline how this system could soon be developed as a platform for implementing more advanced experiments with direct relevance to quantum information processing and quantum thermodynamics, including the study of nanoresonator quantum noise properties, reservoir engineering, and nanomechanical quantum state generation and detection.

No Fine Theorem for Macrorealism: Limitations of the Leggett-Garg Inequality

Tests of local realism and macrorealism have historically been discussed in very similar terms: Leggett-Garg inequalities follow Bell inequalities as necessary conditions for classical behavior. Here, we compare the probability polytopes spanned by all measurable probability distributions for both scenarios and show that their structure differs strongly between spatially and temporally separated measurements. We arrive at the conclusion that, in contrast to tests of local realism where Bell inequalities form a necessary and sufficient set of conditions, no set of inequalities can ever be necessary and sufficient for a macrorealistic description. Fine's famous proof that Bell inequalities are necessary and sufficient for the existence of a local realistic model, therefore, cannot be transferred to macrorealism. A recently proposed condition, no-signaling in time, fulfills this criterion, and we show why it is better suited for future experimental tests and theoretical studies of macrorealism. Our work thereby identifies a major difference between the mathematical structures of local realism and macrorealism.

Observation of Quantum Interference between Separated Mechanical Oscillator Wave Packets

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.

Proposal to Test Bell's Inequality in Electromechanics

Optomechanical and electromechanical systems offer an effective platform to test quantum theory and its predictions at macroscopic scales. To date, all experiments presuppose the validity of quantum mechanics, but could in principle be described by a hypothetical local statistical theory. Here we suggest a Bell test using the electromechanical Einstein-Podolski-Rosen entangled state recently generated by Palomaki et al., Science 342, 710 (2013), which would rule out any local and realistic explanation of the measured data without assuming the validity of quantum mechanics at macroscopic scales. It additionally provides a device-independent way to verify electromechanical entanglement. The parameter regime required for our scheme has been demonstrated or is within reach of current experiments.

Quantum state engineering with circuit electromechanical three-body interactions

We propose a hybrid system with quantum mechanical three-body interactions between photons, phonons, and qubit excitations. These interactions take place in a circuit quantum electrodynamical architecture with a superconducting microwave resonator coupled to a transmon qubit whose shunt capacitance is free to mechanically oscillate. We show that this system design features a three-mode polariton-mechanical mode and a nonlinear transmon-mechanical mode interaction in the strong coupling regime. Together with the strong resonator-transmon interaction, these properties provide intriguing opportunities for manipulations of this hybrid quantum system. We show, in particular, the feasibility of cooling the mechanical motion down to its ground state and preparing various nonclassical states including mechanical Fock and cat states and hybrid tripartite entangled states.