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Hallmarks of quantum mechanics include superposition and entanglement. In the context of large complex systems, these features should lead to situations like Schrodingers cat, which exists in a superposition of alive and dead states entangled with a radioactive nucleus. Such situations are not observed in nature. This may simply be due to our inability to sufficiently isolate the system of interest from the surrounding environment -- a technical limitation. Another possibility is some as-of-yet undiscovered mechanism that prevents the formation of macroscopic entangled states. Such a limitation might depend on the number of elementary constituents in the system or on the types of degrees of freedom that are entangled. One system ubiquitous to nature where entanglement has not been previously demonstrated is distinct mechanical oscillators. Here we demonstrate deterministic entanglement of separated mechanical oscillators, consisting of the vibrational states of two pairs of atomic ions held in different locations. We also demonstrate entanglement of the internal states of an atomic ion with a distant mechanical oscillator.
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Phenomenological models aiming to join gravity and quantum mechanics often predict effects that are potentially measurable in refined low-energy experiments. For instance, modified commutation relations between position and momentum, that accounts for a minimal scale length, yield a dynamics that can be codified in additional Hamiltonian terms. When applied to the paradigmatic case of a mechanical oscillator, such terms, at the lowest order in the deformation parameter, introduce a weak intrinsic nonlinearity and, consequently, deviations from the classical trajectory. This point of view has stimulated several experimental proposals and realizations, leading to meaningful upper limits to the deformation parameter. All such experiments are based on classical mechanical oscillators, i.e., excited from a thermal state. We remark indeed that decoherence, that plays a major role in distinguishing the classical from the quantum behavior of (macroscopic) systems, is not usually included in phenomenological quantum gravity models. However, it would not be surprising if peculiar features that are predicted by considering the joined roles of gravity and quantum physics should manifest themselves just on purely quantum objects. On the base of this consideration, we propose experiments aiming to observe possible quantum gravity effects on macroscopic mechanical oscillators that are preliminary prepared in a high purity state, and we report on the status of their realization.
Engineering nano-mechanical quantum systems possessing ultra-long motional coherence times allow for applications in ultra-sensitive quantum sensing, motional quantum memories and motional interfaces between other carriers of quantum information such as photons, quantum dots and superconducting systems. To achieve ultra-high motional Q one must work hard to remove all forms of motional noise and heating. We examine a magneto-nanomechanical quantum system that consists of a 3D arrangement of miniature superconducting loops which is stably levitated in a static inhomogenous magnetic field. The resulting motional Q is limited by the tiny decay of the supercurrent in the loops and may reach up to Q~10^(10). We examine the classical and quantum dynamics of the levitating superconducting system and prove that it is stably trapped and can achieve motional oscillation frequencies of several tens of MHz. By inductively coupling this levitating object to a nearby flux qubit we further show that by driving the qubit one can cool the motion of the levitated object and in the case of resonance, this can cool the vertical motion of the object close to its ground state.
A complex quantum system can be constructed by coupling simple quantum elements to one another. For example, trapped-ion or superconducting quantum bits may be coupled by Coulomb interactions, mediated by the exchange of virtual photons. Alternatively quantum objects can be coupled by the exchange of real photons, particularly when driven within resonators that amplify interactions with a single electro-magnetic mode. However, in such an open system, the capacity of a coupling channel to convey quantum information or generate entanglement may be compromised. Here, we realize phase-coherent interactions between two spatially separated, near-ground-state mechanical oscillators within a driven optical cavity. We observe also the noise imparted by the optical coupling, which results in correlated mechanical fluctuations of the two oscillators. Achieving the quantum backaction dominated regime opens the door to numerous applications of cavity optomechanics with a complex mechanical system. Our results thereby illustrate the potential, and also the challenge, of coupling quantum objects with light.
Recent progress in observing and manipulating mechanical oscillators at quantum regime provides new opportunities of studying fundamental physics, for example, to search for low energy signatures of quantum gravity. For example, it was recently proposed that such devices can be used to test quantum gravity effects, by detecting the change in the [x,p] commutation relation that could result from quantum gravity corrections. We show that such a correction results in a dependence of a resonant frequency of a mechanical oscillator on its amplitude, which is known as amplitude-frequency effect. By implementing this new method we measure amplitude-frequency effect for 0.3 kg ultra high-Q sapphire split-bar mechanical resonator and for 10 mg quartz bulk acoustic wave resonator. Our experiments with sapphire resonator have established the upper limit on quantum gravity correction constant for $beta_0<5 times10^6$ which is a factor of 6 better than previously detected. The reasonable estimates of $beta_0$ from experiments with quartz resonators yield an even more stringent limit of $4times10^4$. The data sets of 1936 measurement of physical pendulum period by Atkinson results in significantly stronger limitations on $beta_0 ll 1$. Yet, due to the lack of proper pendulum frequency stability measurement in these experiments, the exact upper bound on $beta_0$ can not be reliably established. Moreover, pendulum based systems only allow testing a specific form of the modified commutator that depends on the mean value of momentum. The electro-mechanical oscillators to the contrary enable testing of any form of generalized uncertainty principle directly due to much higher stability and a higher degree of control.
By introducing the thermo entangled state representation, we derived four new photocount distribution formulas for a given density operator of light field. It is shown that these new formulas, which is convenient to calculate the photocount, can be expressed as such integrations over Laguree-Gaussian function with characteristic function, Wigner function, Q-function, and P-function, respectively.
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