Free Nano-Object Ramsey Interferometry for Large Quantum Superpositions

Abstract

We propose an interferometric scheme based on an untrapped nano-object subjected to gravity. The motion of the center of mass (c.m.) of the free object is coupled to its internal spin system magnetically, and a free flight scheme is developed based on coherent spin control. The wave packet of the test object, under a spin-dependent force, may then be delocalized to a macroscopic scale. A gravity induced dynamical phase (accrued solely on the spin state, and measured through a Ramsey scheme) is used to reveal the above spatially delocalized superposition of the spin-nano-object composite system that arises during our scheme. We find a remarkable immunity to the motional noise in the c.m. (initially in a thermal state with moderate cooling), and also a dynamical decoupling nature of the scheme itself. Together they secure a high visibility of the resulting Ramsey fringes. The mass independence of our scheme makes it viable for a nano-object selected from an ensemble with a high mass variability. Given these advantages, a quantum superposition with a 100 nm spatial separation for a massive object of 10^{9} amu is achievable experimentally, providing a route to test postulated modifications of quantum theory such as continuous spontaneous localization.

Pure nanodiamonds for levitated optomechanics in vacuum

“…Optically levitated nanodiamonds containing nitrogen vacancy (NV − ) centre spin defects have been proposed as probes of quantum gravity [1,2], mesoscopic wavefunction collapse [3][4][5][6], phonon mediated spin coupling [7], and the direct detection of dark matter [8,9]. The NV − centre is a point defect in diamond that has a single electron spin which has long coherence times at room temperature and can be both polarized and read out optically [10,11].…”

“…Nanodiamonds containing NV − centres have been trapped using ion traps at atmospheric pressure [17,18] and in vacuum [19], and a magneto-gravitational trap has allowed nanodiamond clusters to be held below 10 −2 mbar [20]. However, the latter design requires permanent magnets for the levitation, which is incompatible with the trap-and-release experiments [1,2,6] that reach large distance spatial superpositions of the centre-of-mass as desired for all of the fundamental physics experiments mentioned above.…”

Bose et al. Reply:

“…Nonetheless, the fact that indeed there was a time varying spatial separation between |β(t, +1) and |β(t, −1) can be concluded from a time modulation e −( 2 (1−cos ωzt) of the visibility of φ + (t) − φ − (t) from the spin state alone [5,6]. Moreover, the spin dependent position splitting can be enhanced by a lower ω z or free flight [7] if one feels that an independent verification of the Stern-Gerlach effect through spin-position correlation measurements is truly necessary. …”

Displacemon Electromechanics: How to Detect Quantum Interference in a Nanomechanical Resonator

“…1 may be particularly experimentally favorable for this implementation because they imply that the coupling exceeds both the thermal decay rate of the resonator and the typical dephasing rate of a qubit (see Appendix E). Importantly, our scheme does not rely on degeneracy between the qubit and the resonator [15], nor on qubit coherence over the lifetime of the mechanical superposition [72].…”

“…Although the nanotube resonator considered here does not have enough mass to seriously challenge the interesting parameter regime of objective collapse theories, a similar protocol could be extended to more massive objects still well within the range of nanomechanics. This research direction could allow for testing specific theories of quantum collapse [8], as an alternative to proposals based on single-photon optomechanics [9] or levitated nanoparticles [11,72]. Multiple resonators coupled to the same qubit (such as the pair of nanotube junctions in Fig.…”