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arXiv:2211.10318 · Physical Review Letters

Mass-Independent Scheme to Test the Quantumness of a Massive Object

Debarshi Das, Dipankar Home, Hendrik Ulbricht, Sougato Bose

Published Jan 16, 2024• 8 citations
arXivHTMLPDF

Abstract

The search for empirical schemes to evidence the nonclassicality of large masses is a central quest of current research. However, practical schemes to witness the irreducible quantumness of an arbitrarily large mass are still lacking. To this end, we incorporate crucial modifications to the standard tools for probing the quantum violation of the pivotal classical notion of macrorealism (MR): while usual tests use the same measurement arrangement at successive times, here we use two different measurement arrangements. This yields a striking result: a mass-independent violation of MR is possible for harmonic oscillator systems. In fact, our adaptation enables probing quantum violations for literally any mass, momentum, and frequency. Moreover, coarse-grained position measurements at an accuracy much worse than the standard quantum limit, as well as knowing the relevant parameters only to this precision, without requiring them to be tuned, suffice for our proposal. These should drastically simplify the experimental effort in testing the nonclassicality of massive objects ranging from atomic ions to macroscopic mirrors in LIGO.

DOI
10.1103/physrevlett.132.030202

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The search for empirical schemes to evidence the nonclassicality of large masses is a central quest of current research. However, practical schemes to witness the irreducible quantumness of an arbitrarily large mass are still lacking. To this end, we incorporate crucial modifications to the standard tools for probing the quantum violation of the pivotal classical notion of macrorealism (MR): while usual tests use the same measurement arrangement at successive times, here we use two different measurement arrangements. This yields a striking result: a mass-independent violation of MR is possible for harmonic oscillator systems. In fact, our adaptation enables probing quantum violations for literally any mass, momentum, and frequency. Moreover, coarse-grained position measurements at an accuracy much worse than the standard quantum limit, as well as knowing the relevant parameters only to this precision, without requiring them to be tuned, suffice for our proposal. These should drastically simplify the experimental effort in testing the nonclassicality of massive objects ranging from atomic ions to macroscopic mirrors in LIGO.
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.
An open challenge in physics is to expand the frontiers of the validity of quantum mechanics by evidencing nonclassicality of the centre of mass state of a macroscopic object. Yet another equally important task is to evidence the essential nonclassicality of the interactions which act between macroscopic objects. Here we introduce a new tool to meet these challenges: massive spatial qubits. In particular, we show that if two distinct localized states of a mass are used as the ∣0⟩|0\rangle∣0⟩ and ∣1⟩|1\rangle∣1⟩ states of a qubit, then we can measure this encoded spatial qubit with a high fidelity in the σx,σyσ_x, σ_yσx​,σy​ and σzσ_zσz​ bases simply by measuring its position after different durations of free evolution. We show how this technique can be used to reveal an irreducible nonclassicality through a Bell-inequality violation arising from the entanglement of the centre of mass of a nano-crystal with its spin in a Stern-Gerlach setup. Secondly, we show how our methodology, in conjuction with the Casimir interaction, offers a powerful method to create and certify non-Gaussian entanglement between two neutral nano-objects. Fundamentally, the generation of such an entanglement provides an empirical means for demonstrating an inherent quantumness of the Casimir interaction.
An open challenge in physics is to expand the frontiers of the validity of quantum mechanics by evidencing nonclassicality of the center of mass state of a macroscopic object. Yet another equally important task is to evidence the essential nonclassicality of the interactions which act between macroscopic objects. Here we introduce a new tool to meet these challenges: massive spatial qubits. In particular, we show that if two distinct localized states of a mass are used as the $|0\ensuremath{\rangle}$ and $|1\ensuremath{\rangle}$ states of a qubit, then we can measure this encoded spatial qubit with a high fidelity in the ${\ensuremath{\sigma}}_{x},{\ensuremath{\sigma}}_{y}$, and ${\ensuremath{\sigma}}_{z}$ bases simply by measuring its position after different duration of free evolution. This technique can be used reveal the irreducible nonclassicality of the spin and center of mass entangled state of a nanocrystal implying macrocontextuality. Further, in the context of Casimir interaction, this offers a powerful method to create and certify non-Gaussian entanglement between two neutral nano-objects. The entanglement such produced provides an empirical demonstration of the Casimir interaction being inherently quantum.
We propose an experimental scheme to test the nonclassicality of a macroscopic ensemble of qubits, through the violation of the classical notion of macrorealism (MR) via the fundamental measurement-induced disturbance of quantum systems. An electromagnetic resonator is used to probe the parity of the qubit-ensemble. The action of sequential measurements allows the nonclassicality of whole ensemble to manifest itself, in the ideal case, irrespective of its size. This enables to probe the macroscopic limits of quantum mechanics as the qubit-ensemble is, effectively, a single large spin of many ℏ\hbarℏ units. Even as ℏ→0\hbar \rightarrow 0ℏ→0 in comparison to the total angular momentum of the ensemble, a constant amount of violation of MR is found in the noiseless case. However, environmental decoherence and inhomogeneity of qubit-electromagnetic field couplings precipitate the quantum-to-classical transition. This illustrates that Bohr's correspondence principle is not fundamental, but a consequence of practical limitations. We outline an implementation with a variety of qubits (superconducting qubits, spins in semiconductors, and Rydberg atoms) coupled to a coplanar waveguide resonator, and -- via the corresponding noise analysis -- find that violation of MR is detectable up to 100100100 qubits via current technology.
I study several aspects of tests of macrorealism (MR), which for a given data set serves to give a quantitative signal of the presence of a specific notion of non-classical behaviour. The insufficiency of classical understanding underpins both the paradoxes of quantum mechanics, its future technological promise, and so these tests are of interest both foundationally and pragmatically. I derive generalisations of the Leggett-Garg (LG) inequalities and Fine's theorem, which together establish the necessary and sufficient conditions for macrorealism. First, I extend these conditions to tests involving an arbitrary number of measurement times. Secondly, I generalise them beyond the standard dichotomic variable, to systems described by many-valued variables. I also perform a quantum mechanical analysis examining the interplay of different conditions of MR. I then develop the theoretical framework to support tests of macrorealism in continuous variable systems, where I define variables based on coarse-grainings of position. I calculate temporal correlators for general bound systems, and analyse LG violations within the quantum harmonic oscillator (QHO), in its energy eigenstates and coherent states. I analyse the precise physical mechanisms underpinning the violations in terms of probability currents, Bohm trajectories. Staying within continuous variable systems, we outline a different approach to meeting the invasiveness requirement of LG tests. Reasoning that we may approximately non-invasively measure whether a particle crosses the axis, we measure an object which is related to the standard correlators, and derive a set of macrorealistic inequalities for these modified correlators. We demonstrate violations of these modified LG inequalities for several states within the QHO.
For testing quantum mechanics in the macroscopic domain, a major challenge is to devise effective means for enhancing the observable nonclassical signatures despite the ubiquitous presence of environmental decoherence. Toward this goal, we invoke the Quantum Zeno Effect (QZE) for achieving a tunable amplification of an inherently nonclassical quantum disturbance induced by any measurement. Such an enhancement of otherwise small and decoherence-suppressed nonclassicality can arise from the cumulative quantum disturbances generated by repetitive measurements, with the tunability of amplification controlled by the number of measurements. To evidence this, we formulate a testable loophole-free scheme using a massive oscillator, where the system preparation requires trapping and ground-state cooling of a massive object. The required measurements can be realized through a beam-splitter-type interaction between the mechanical oscillator and an optical field, followed by photon detection. Our analysis shows that such amplification, suitably quantified in terms of a testable witness, remains appreciably observable even in the realistic regimes of optomechanical damping, and for sufficiently large masses, thus enabling the demonstration of QZE in the macroscopic domain.