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Physical Review Research

Massive spatial qubits: Testing macroscopic nonclassicality and Casimir entanglement

Bin Yi, Urbasi Sinha, Dipankar Home, Anupam Mazumdar, Sougato Bose

Published Sep 22, 2023• 5 citations
Publisher

Abstract

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.

DOI
10.1103/physrevresearch.5.033202

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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⟩|0\ensuremath{\rangle}∣0\ensuremath⟩ and ∣1\ensuremath⟩|1\ensuremath{\rangle}∣1\ensuremath⟩ states of a qubit, then we can measure this encoded spatial qubit with a high fidelity in the \ensuremathσx,\ensuremathσy{\ensuremath{\sigma}}_{x},{\ensuremath{\sigma}}_{y}\ensuremathσx​,\ensuremathσy​, and \ensuremathσz{\ensuremath{\sigma}}_{z}\ensuremathσz​ 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.
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.
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.
Abstract Witnessing the quantum nature of gravity through the entanglement of two masses has recently been proposed. Both non-Gaussian and Gaussian protocols have been shown to be useful for this purpose. In non-Gaussian protocols the complete 1 / r gravitational interaction can in principle be utilized for entanglement generation, as long as quantum superpositions of a spatial splitting Δ x comparable to the distance d between two masses can be generated. In practice, however, all non-Gaussian protocols proposed to date rely on embedded qubits—typically spins—to read out the entanglement: spin correlations are used to witness the entanglement developed between the masses during interferometry. Here we show that if superpositions of distinct spatially localized states of each mass can be created, then a spinless version of the non-Gaussian protocol is possible: simple position correlation measurements alone can yield a spatial qubit witness of the entanglement between the masses. We find that the principal new requirement for the viability of this protocol is a position squeezing of the wavefunction by approximately seven orders of magnitude, applied at a specific stage of the experiment.
Quantum entanglement provides a novel way to test short distance physics in the nonrelativistic regime. We will provide a protocol to potentially test new physics by bringing two charged massive particle interferometers adjacent to each other. Being charged, the two superpositions will be entangled via electromagnetic interactions mediated by the photons, including the Coulomb and the Casimir-Polder potential. We will bring a method of entanglement based tomography to seek time evolution of very small entanglement phases to probe new physical effects mediated by hitherto unknown macroscopic force which might be responsible for entangling the two charged superpositions modeled by the Yukawa type potential. We will be able to constrain the Yukawa couplings $\ensuremath{\alpha}\ensuremath{\ge}{10}^{\ensuremath{-}35}$ for $r\ensuremath{\ge}{10}^{\ensuremath{-}6}\text{ }\text{ }\mathrm{m}$ for new physics occurring in the electromagnetic sector, and in the gravitational potential ${\ensuremath{\alpha}}_{g}\ensuremath{\ge}{10}^{\ensuremath{-}8}$ for $r\ensuremath{\ge}{10}^{\ensuremath{-}6}\text{ }\text{ }\mathrm{m}$. Furthermore, our protocol can also constrain the axionlike particle mass and coupling, which is complimentary to the existing experimental bounds.
A previously unexplored scheme is devised for creating and certifying coherent quantum superposition of distinctly separated states of a spin-tagged massive object passing through a confined uniform magnetic field. This results in entangling the spatial and spin parts of a two-component Pauli wavefunction such that the entailed coherence can be conveniently certified by spin measurements alone. The implementability of this scheme is analysed using NV-centre nanodiamonds of masses ∼1010\sim 10^{10}∼1010 amu based on the current technological capabilities.
Over the past few decades, experimental tests of Bell-type inequalities have been at the forefront of understanding quantum mechanics and its implications. These strong bounds on specific measurements on a physical system originate from some of the most fundamental concepts of classical physics-in particular that properties of an object are well-defined independent of measurements (realism) and only affected by local interactions (locality). The violation of these bounds unambiguously shows that the measured system does not behave classically, void of any assumption on the validity of quantum theory. It has also found applications in quantum technologies for certifying the suitability of devices for generating quantum randomness, distributing secret keys and for quantum computing. Here we report on the violation of a Bell inequality involving a massive, macroscopic mechanical system. We create light-matter entanglement between the vibrational motion of two silicon optomechanical oscillators, each comprising approx. 10^{10} atoms, and two optical modes. This state allows us to violate a Bell inequality by more than 4 standard deviations, directly confirming the nonclassical behavior of our optomechanical system under the fair sampling assumption.