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arXiv:2106.11906

Massive Spatial Qubits for Testing Macroscopic Nonclassicality and Casimir Induced Entanglement

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

Published Jun 22, 2021• 1 citation
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Abstract

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 $|0\rangle$ and $|1\rangle$ states of a qubit, then we can measure this encoded spatial qubit with a high fidelity in the $σ_x, σ_y$ and $σ_z$ 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.

DOI
10.48550/arxiv.2106.11906

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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 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.
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.
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.
Quantum entanglement provides a novel way to test short-distance quantum physics in a non-relativistic regime. We provide entanglement-based protocols to potentially test the magnetically induced dipole-dipole interaction and the Casimir-Polder potential between the two nano-crystals kept in a Schrodinger Cat state. Our scheme is based on the Stern-Gerlach (SG) apparatus, where we can witness the entanglement mediated by these interactions for the nano-crystal mass m~10^-19 kg with a spatial superposition size of order 0.1 micron in a trap relying on diamagnetic levitation. We show that it is possible to close the SG interferometer in position and momentum with a modest gradient in the magnetic field.
We propose an experiment to test Bell nonlocality, a genuine nonclassicality, for the gravitational field. Two masses with embedded entangled spins (e.g., two diamonds with their NV-centre spins entangled) are placed well outside each other's light cones, ensuring a locality-loophole-free scenario. The spins are then coupled to the motion of their respective masses to generate spatial superpositions. Finally, local measurements are performed only on the gravitational fields of the two masses. If gravity is quantum, then the two entangled masses would entangle their gravitational fields, leading to correlations certifying Bell nonlocality of gravity. Trapped and ground-state cooled nano-objects with micron-sized spatial superposition are sufficient for this test. This goes beyond the recent proposals to test nonclassicality of gravity by providing, for the first time in the literature, a minimal tool to (i) create Einstein-Podolsky-Rosen (EPR) state of gravitational curvatures, (ii) witness entangled gravitational curvatures, (iii) rule out any local-realist description of gravity, and (iv) achieve a loophole-free test of gravity's nonclassicality in a fully device-independent way.
We analytically solve the entangling quantum dynamics of two interacting Stern-Gerlach Interferometers~(SGI). Each SGI exploits an operator-valued force applied by a qubit to create and recombine a non-Gaussian state of matter. The entangling phase between the two qubits generated by the leading-order gravitational interaction of the massive degrees of freedom is found to be mass-independent, both for unitary and open dynamics, irrespective of the temperature and squeezing of the initial states. Further, we show that the solution of the four interferometric paths reveals that the mere presence of the interaction does not allow for a perfect recombination of the centre of mass. This second-order effect, alongside higher-order interaction terms, can be used to bound the mass from above and below, thus restricting the experiment's regime to mesoscopic masses. By solving the open dynamics which includes diffusion and dephasing with initial squeezed thermal states, the bounds are tightened by the inclusion of realistic experimental noise. We discuss diamagnetic levitated masses with embedded NV-centres as a specific physical implementation.