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arXiv:1912.08159 · Physical Review A

Perturbative algorithm for rotational decoherence

Matteo Carlesso, Hamid Reza Naeij, Angelo Bassi

Published Mar 25, 2021• 3 citations
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Abstract

Recent advances in levitated optomechanics provide new perspectives for the use of rotational degrees of freedom for the development of quantum technologies as well as for testing fundamental physics. As for the translational case, their use, especially in the quantum regime, is limited by environmental noises, the characterization of which is fundamental in order to assess, control, and minimize their effect, in particular decoherence. Here, we present a general perturbative approach to compute decoherence for a quantum system in a superposition of its rotational degrees of freedom. The specific cases of the dipole-dipole and quadrupole-quadrupole interactions are solved explicitly, and we show that the rotational degrees of freedom decohere on a time scale that can be longer than the translational one.

DOI
10.1103/physreva.103.032220

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Recent advances in levitated optomechanics provide new perspectives for the use of rotational degrees of freedom for the development of quantum technologies as well as for testing fundamental physics. As for the translational case, their use, especially in the quantum regime, is limited by environmental noises, the characterization of which is fundamental in order to assess, control, and minimize their effect, in particular decoherence. Here, we present a general perturbative approach to compute decoherence for a quantum system in a superposition of its rotational degrees of freedom. The specific cases of the dipole-dipole and quadrupole-quadrupole interactions are solved explicitly, and we show that the rotational degrees of freedom decohere on a time scale that can be longer than the translational one.
The mechanism of decoherence for a mesoscopic quantum system with rotational degrees of freedom is studied. From a simple model of elastic scattering, we show that the nondiagonal density-matrix elements of the system exponentially decay. The decay rate depends on the difference of scattering amplitudes for different rotational configurations, leading to the gradual loss of quantum coherence between the pointer states in the orientational space. For a dielectric ellipsoid immersed in a photon-gas environment (assuming no absorption), the decay rate is found to be proportional to the seventh power of the temperature. For an ellipsoidal object interacting with massive particles, the decay rate is proportional to the 5/2 power of the temperature. Both are different from the case of translational decoherence induced by the same environment scattering. For photon scattering, the coherence time in the rotational degrees of freedom is shown to be much shorter than that in the translational degrees of freedom.
The dynamics of non-polar diatomic molecules interacting with a far-detuned narrow-band laser field, that only may drive rotational transitions, is studied. The rotation of the molecule is considered both classically and quantum mechanically, providing links to features known from the heavy symmetric top. In particular, quantum decoherence in the molecular rotation, induced by spontaneous Raman processes, is addressed. It is shown how this decoherence modifies the rotational dynamics in phase space.
The use of rotational degrees of freedom of quantum systems in quantum technologies is limited by environmental effects under decoherence mechanism. Here, we study the mechanism of decoherence based on a new formalism of elastic scattering for a nonspherical quantum system prepared in a superposition of rotational degrees of freedom. We show that for a dielectric ellipsoid immersed in an environment composed of thermal photons the rotational decoherence rate depends on the angular differences between the two configurations of the system and the seventh power of the temperature which is different from the translational one. Then we analyze the effect of different values of angular momentum quantum numbers of the environmental spherical harmonics on the rotational decoherence rate.
Laboratory-based experimental tests remain a central challenge in the study of the quantum-gravity interface. We present a quantitative, experimentally testable prediction for gravitationally induced quantum decoherence of spatial superpositions in levitated optomechanical systems. Starting from two independently well-tested physical elements—the quantum nature of material energy-momentum fluctuations (established in particle physics) and the linear response kernel of classical geometry (derived from the weak-field limit of general relativity and verified by gravitational-wave observations)—and supplementing them with a minimal extension postulate for superposition states, we obtain a rigid scaling law for the gravitational decoherence rate: \Gamma \sim G M^2 d^2 / (\hbar L^3) \cdot \Phi(l_*/L), where M is the mass of the object, d the spatial separation of the superposition branches, L the characteristic linear dimension, and \Phi a dimensionless function encoding the unknown ultraviolet cutoff scale l_* of the effective geometric noise. The structural form \Gamma \propto M^2 d^2 / L^3 contains no free adjustable parameters; the overall amplitude is set by the choice of l_*. Identifying l_* with the Planck length \ell_P = \sqrt{\hbar G / c^3}—the only known scale bridging quantum theory and gravity—yields \Phi \sim \mathcal{O}(1) and a specific numerical target. For current levitated nanoparticle experiments (M \sim 10^{-14}\,\text{kg}, d \sim 10^{-7}\,\text{m}, L \sim 10^{-6}\,\text{m}), this Planck-scale hypothesis predicts a decoherence rate of order 1\,\text{Hz}, placing it within the foreseeable sensitivity window of next-generation optomechanical setups. We discuss the exclusive physical signatures distinguishing this mechanism from environmental decoherence channels and outline explicit falsification conditions, providing experimental groups with a concrete target to probe the quantum-gravity interface in the laboratory.
We employ spherical t-designs for the systematic construction of solids whose rotational degrees of freedom can be made robust to decoherence due to external fluctuating fields while simultaneously retaining their sensitivity to signals of interest. Specifically, the ratio of signal phase accumulation rate from a nearby source to the decoherence rate caused by fluctuating fields from more distant sources can be incremented to any desired level by using increasingly complex shapes. This allows for the generation of long-lived macroscopic quantum superpositions of rotational degrees of freedom and the robust generation of entanglement between two or more such solids with applications in robust quantum sensing and precision metrology as well as quantum registers.
Levitated nanoparticles, free from the clamping losses and decoherence channels imposed by mechanical support, offer a growing versatile platform for precision sensing and tests of fundamental physics at increasingly larger masses. This thesis follows complementary directions based on this platform: the coupling of optically controllable nuclear spin ensembles to the mechanical and rotational degrees of freedom of levitated solids, and the identification of decoherence mechanisms that limit levitated systems in tests of macroscopic quantum superpositions. In the first part, we study levitated solids doped with non-permanent, optically addressable electron spins, with pentacene-doped naphthalene as a prime exam ple, whose nuclear spins can be hyperpolarised using dynamic nuclear polarisation techniques to over 80% at cryogenic temperatures, with lifetimes extending over weeks. Exploiting the homogeneous spin distribution and absence of a preferred nuclear quantisation axis in such materials, we design a multi-spin Stern-Gerlach interferometry protocol that circumvents key limitations of colour centres in nan odiamonds like NV centres, and use it to place improved bounds on objective collapse models. We further show that the unconstrained rotation available to levitated particles enables magic angle spinning at frequencies beyond current NMRstandards, and propose a protocol for reading out spin ensemble polarisation directly from the particle’s mechanical motion. Building on the same hyperpo larisation mechanism, we propose experiments to observe the nuclear Einstein-de Haas effect, using the hyperpolarised bath of nuclei as a reservoir for angular mo mentum. Furthermore, we propose a protocol to investigate the nuclear Barnett effect in the solid state, using the MHz-scale rotation rates accessible to levitated particles. We find that the proposed Stern-Gerlach interferometer could improve upon existing bounds on collapse-model parameters and that the nuclear Einstein de Haas and Barnett effects could be observable using near-term experimental technology, within parameter ranges already accessible to the community. In the second part, we turn to a central obstacle facing proposals for gravitationally induced entanglement (GIE) between levitated masses, namely the conducting and magnetic shields required to suppress direct electromagnetic coupling. We show that residual Casimir and magnetic-dipole interactions between the particles and the shield, averaged over run-to-run positional and orientational fluctuations of the experimental set-up, generate decoherence, and that the shield can itself mediate spurious entanglement between the particles that might mimic a genuine gravitational-entanglement signature. From this, we derive quantitative stability thresholds considerably stricter than previously assumed.