Bose et al. Reply:

Abstract

Our papers [1,2] propose an experiment in which the observation of Ramsey fringes would be evidence for a spatial superposition. We analyzed this as a magnetic effect creating a Stern-Gerlach like spin dependent separation of the centre of mass (COM) states in conjunction with a gravitational effect imparting a relative phase between the states. The comment points out that this could be interpreted in a different way. It contends that the interference manifested in the spin states is not due to the spatial separation as the gravity effects can also be interpreted as a Zeeman effect. To support its contention, the comment splits the Hamitonian into parts H 1 and H 2 where only H 1 couples the COM with the spin states, while H 2 imparts the phase factor. However, the periodic factorizability of the COM and the spin states requires the action of H 1 as well. It is this factorizability which makes the phase detectable by a measurement on the spin alone. For instance, if the COM and spin states are not entangled at T /2, the evolution by H 1 alone for an additional time T /2 will not be able to factorise them. This will lead to the Ramsey interference pattern being supressed. Thus the very visibility of the phase due to H 2 hinges on the interference brought about by H 1 . Both treatments (our's and the comment's) are valid and equivalent as they use the same Hamiltonian. In both cases there is a spatial superposition except for certain periodic moments in time (at integer multiples of the oscillator time period T ). In both cases, the absence of coherence in the COM motion (which could be due to decoherence from air molecules for example) would remove these fringes.In the absence of decoherence, an arbitrary initial coherent state |β of the COM and an initial spin statewhere |β(t, ±1) are COM coherent states with the timevarying separation of ∆z(t) = 8λδz ωz (1 − cos ω z t) with δ z = 2mωz being the ground state position spread of the oscillator. Despite the fact that |β(t, ±1) oscillate about centresωz where there are finite magnetic fields, in our approach, the entire inhomogeneous magnetic field term of the Hamitonian is "used up" to accompish the Stern-Gerlach like separation ∆z(t), and is thereby, not available any more to impart a Zeeman phase between the separated states. The integrated gravitational phase shift T 0 mg cos θ∆z(t)dt gives exactly theLet us now clarify that even if the comment's interpretation that the measured signal results from "the common displacement of the COM position of both ±1 states" is adopted, the visibility of this signal is affected by the coherence between the superposed COM states. Consider a case where only the COM motion is decohered: the off diagonal terms |β(t, +1) β(t, −1)| are damped by a factor of e −γ(t) . Then the evolved state at t = N T isThus we see that the spin density matrix has also decohered (thereby lowering the visibility of φ as a relevant parameter, say θ, is varied) despite the fact that the decoherence was exclusively for the COM state [3,4]. In particular...

When can gravity path-entangle two spatially superposed masses?

“…Recently, a different class of tests has been introduced, based on an indirect method [3,4], which is not affected by such difficulties. Instead of measuring directly quanta of the gravitational field, the proposal is to test the ability of the gravitational field to entangle two masses each in a superposition of two different locations.…”

Non-Gaussian mechanical motion via single and multi-phonon subtraction from a thermal state

“…Pursuing this line of research will facilitate the development of mechanical-oscillator-based quantum technology components such as quantum memories exploiting the long coherence times available [1][2][3], coherent transducers [4,5], and sensors [6][7][8]. Additionally, such state generation and reconstruction capabilities will help enable tests of fundamental physics including exploring the quantum-toclassical transition [9][10][11] and even studying the interface between quantum mechanics and gravity [12][13][14].…”

Vindication of entanglement-based witnesses of non-classicality in hybrid systems

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Recently, Vedral and one of us proposed an entanglement-based witness of non-classicality in systems that need not obey quantum theory, based on constructor-information-theoretic ideas [1,3], which offers a robust foundation for recently proposed table-top tests of non-classicality in gravity, [2,3]. The witness asserts that if a mediator can entangle locally two quantum systems, then it has to be non-classical.

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“…Recently, an experimental scheme has been proposed in order to refute classical theories of gravity in the presence of quantum masses, [2,3]. This scheme is based on probing gravity with two masses, each in a superposition.…”