A Nanoscale Experiment Measuring Gravity's Role in Breaking the Unitarity of Quantum Dynamics

Modern, state of the art nanomechanical devices are capable of creating spatial superpositions that are massive enough to begin to experimentally access the quantum to classical crossover, and thus force us to consider the possible ways in which the usual quantum dynamics may be affected. One recent theoretical proposal describes the crossover from unitary quantum mechanics to classical dynamics as a form of spontaneous symmetry breaking. Here, we propose a specific experimental setup capable of identifying the source of unitarity breaking in such a mechanism. The experiment is aimed specifically at clarifying the role played by gravity, and distinguishes the resulting dynamics from that suggested by alternative scenarios for the quantum to classical crossover. We give both a theoretical description of the expected dynamics, and a discussion of the involved experimental parameter values and the proposed experimental protocol.Comment: 11 pages, 5 figures; final versio

A Tunable Kondo Effect in Quantum Dots

We demonstrate a tunable Kondo effect realized in small quantum dots. We can switch our dot from a Kondo impurity to a non-Kondo system as the number of electrons on the dot is changed from odd to even. We show that the Kondo temperature can be tuned by means of a gate voltage as a single-particle energy state nears the Fermi energy. Measurements of the temperature and magnetic field dependence of a Coulomb-blockaded dot show good agreement with predictions of both equilibrium and non-equilibrium Kondo effects.Comment: 8 pages, 4 figure

Current experimental upper bounds on spacetime diffusion

A consistent theory describing the dynamics of quantum systems interacting on a classical space-time was recently put forward by Oppenheim et al..[1, 2]. Quantum states may retain their coherence, at the cost of some amount of stochasticity of the spacetime metric, characterized by a spacetime diffusion parameter. Here, we report existing experimental upper bounds on such space-time diffusion, based on a review of several types of experiments with very low force noise over a broad range of test masses from single atoms to several kilograms. We find an upper bound at least 15 orders of magnitude lower as compared to the initial bounds for explicit models presented by Oppenheimn et al. The results presented here provide a path forward for future experiments that can help evaluate classical-quantum theoriesComment: 8 pages, 1 figure, 1 tabl

Vibration isolation with high thermal conductance for a cryogen-free dilution refrigerator

We present the design and implementation of a mechanical low-pass filter vibration isolation used to reduce the vibrational noise in a cryogen-free dilution refrigerator operated at 10 mK, intended for scanning probe techniques. We discuss the design guidelines necessary to meet the competing requirements of having a low mechanical stiffness in combination with a high thermal conductance. We demonstrate the effectiveness of our approach by measuring the vibrational noise levels of an ultrasoft mechanical resonator positioned above a SQUID. Starting from a cryostat base temperature of 8 mK, the vibration isolation can be cooled to 10.5 mK, with a cooling power of 113 $\mu$W at 100 mK. We use the low vibrations and low temperature to demonstrate an effective cantilever temperature of less than 20 mK. This results in a force sensitivity of less than 500 zN/$\sqrt{\mathrm{Hz}}$, and an integrated frequency noise as low as 0.4 mHz in a 1 Hz measurement bandwidth

Measuring gravity with milligram levitated masses

Gravity differs from all other known fundamental forces since it is best described as a curvature of spacetime. For that reason it remains resistant to unifications with quantum theory. Gravitational interaction is fundamentally weak and becomes prominent only at macroscopic scales. This means, we do not know what happens to gravity in the microscopic regime where quantum effects dominate, and whether quantum coherent effects of gravity become apparent. Levitated mechanical systems of mesoscopic size offer a probe of gravity, while still allowing quantum control over their motional state. This regime opens the possibility of table-top testing of quantum superposition and entanglement in gravitating systems. Here we show gravitational coupling between a levitated sub-millimeter scale magnetic particle inside a type-I superconducting trap and kg source masses, placed approximately half a meter away. Our results extend gravity measurements to low gravitational forces of attonewton and underline the importance of levitated mechanical sensors. Specifically, at a frequency of 26.7 Hz, a mass of 0.4 mg and showing Q-factors in excess of 10$^7$, we obtained a force noise of 0.5 $fN\sqrt{Hz}$ . We simultaneously detect the other 5 rotational and translational degrees of freedom.Comment: 13 pages, with 13 pages supplementary material

Towards an experimental test of gravity-induced quantum state reduction

According to the hypothesis of Penrose and Diosi, quantum state reduction is a manifestation of the incompatibilty of general relativity and the unitary time evolution of quantum physics. Dimensional analysis suggests that Schrodinger cat type states should collapse on measurable time scales when masses and lengths of the order of bacterial scales are involved. We analyze this hypothesis in the context of modern developments in condensed matter and cold atoms physics, aimed at realizing macroscopic quantum states. We first consider 'micromechanical' quantum states, analyzing the capacity of an atomic force microscopy based single spin detector to measure the gravitational state reduction, but we conclude that it seems impossible to suppress environmental decoherence to the required degree. We subsequently discuss 'split' cold atom condensates to find out that these are at present lacking the required mass scale by many orders of magnitude. We then extent Penrose's analysis to superpositions of mass current carrying states, and we apply this to the flux quantum bits realized in superconducting circuits. We find that the flux qubits approach the scale where gravitational state reduction should become measurable, but bridging the few remaining orders of magnitude appears to be very difficult with present day technology.Comment: 12 pages, 7 figure

Size of the Localized Electron Emission Sites on a Closed Multiwalled Carbon Nanotube

036804Quantum Matter and Optic