Two quantum Macro-states and their Macroscopic Quantum Superpositions (MQS) localized in two far apart, space - like separated sites can be non-locally correlated by any entangled couple of single-particles having interacted in the past. This novel Macro - Macro paradigm is investigated on the basis of a recent study on an entangled Micro-Macro system involving N=10^5 particles. Crucial experimental issues as the violation of Bell's inequalities by the Macro - Macro system are considered.
We consider the collapse of a macroscopic quantum superposition occurring due to the measurement which optimally distinguishes its branches. Given a macroscopic superposition of N spin-1/2 particles, we use such a Helstrom measurement to construct the local unitary operator which maximizes the usefulness of the superposition for Heisenberg-limited phase estimation (i.e., with quantum Cramér Rao bound proportional to 1/N). In contrast, the collapsed state is not useful as a probe for phase estimation below the standard quantum limit. For the case N=2, we compute the entanglement entropy of the …
We utilise a magneto-mechanical levitated massive resonator in the quantum regime to prepare highly macroscopic quantum superposition states. Using these macroscopic superpositions we present a novel interferometry protocol to perform absolute gravimetry with a sensitivity that exceeds state of the art atom-interferometric and corner-cube gravimeters by a factor of 20. In addition, our scheme allows probing the gravitational field on a length scale eight orders of magnitude smaller than other methods.
We suggest a way to quantify a type of macroscopic entanglement via distillation of Greenberger-Horne-Zeilinger states by local operations and classical communication. We analyze how this relates to an existing measure of quantum macroscopicity based on the quantum Fisher information in several examples. Both cluster states and Kitaev surface code states are found to not be macroscopically quantum but can be distilled into macroscopic superpositions. We look at these distillation protocols in more detail and ask whether they are robust to perturbations. One key result is that one-dimensional c…
We study the question of what kind of a macroscopic superposition can(not) naturally exist as a ground state of some gapped local many-body Hamiltonian. We derive an upper bound on the energy gap of an arbitrary physical Hamiltonian provided that its ground state is a superposition of two well-distinguishable macroscopic "semi-classical" states. For a large class of macroscopic superposition states we show that the gap vanishes in the macroscopic limit. This in turn shows that preparation of such states by simple cooling to the ground state is not experimentally feasible and requires different…
We consider fundamental limits on the detectable size of macroscopic quantum superpositions. We argue that a full quantum mechanical treatment of system plus measurement device is required, and that a (classical) reference frame for phase or direction needs to be established to certify the quantum state. When taking the size of such a classical reference frame into account, we show that to reliably distinguish a quantum superposition state from an incoherent mixture requires a measurement device that is quadratically bigger than the superposition state. Whereas for moderate system sizes such a…
Quantum entanglement is the quintessence of quantum information processing mostly limited to the microscopic regime governed by Heisenberg uncertainty principle. For practical applications, however, macroscopic entanglement gives great benefits in both photon loss and sensitivity. Recently, a novel method of macroscopic entanglement generation has been proposed and demonstrated in a coupled interferometric system using classical laser light, where superposition between binary bases in each interferometric system plays a key role. Here, the function of path superposition applied to independent …
Quantum superposition in mechanical systems is not only key evidence for macroscopic quantum coherence, but can also be utilized in modern quantum technology. Here we propose an efficient approach for creating macroscopically distinct mechanical superposition states in a two-mode optomechanical system. Photon hopping between the two cavity modes is modulated sinusoidally. The modulated photon tunneling enables an ultrastrong radiation-pressure force acting on the mechanical resonator, and hence significantly increases the mechanical displacement induced by a single photon. We study systematica…
We establish an objective scheme to determine the macroscopicity of quantum mechanical superposition tests, which is based on the Bayesian hypothesis falsification of macrorealistic modifications of quantum theory. The measure uses the raw data gathered in an experiment, taking into account all measurement uncertainties, and can be used to directly assess any conceivable quantum test. We determine the resulting macroscopicity for three recent tests of quantum physics: double-well interference of Bose-Einstein condensates, Leggett-Garg tests with atomic random walks, and entanglement generation…
We describe a set of measurement protocols for performing non-classicality tests and the verification of entangled superposition states of macroscopic continuous variable systems, such as nanomechanical resonators. Following earlier works, we first consider a setup where a two-level system is used to indirectly probe the motion of the mechanical system via Ramsey measurements and discuss the application of this methods for detecting non-classical mechanical states. We then show that the generalization of this techniques to multiple resonator modes allows the conditioned preparation and the det…
It is well known that in a quantum phase transition (QPT), entanglement remains short ranged [Osterloh et al., Nature 416 608-610 (2005)]. We ask if there is a quantum property entailing the whole system which diverges near this point. Using the recently proposed measures of quantum macroscopisity, we show that near a quantum critical point, it is the effective size of macroscopic superposition between the two symmetry breaking states which grows to the scale of system size and its derivative with respect to the coupling shows both singular behavior and scaling properties.
Superposition states are at the origin of many paradoxes in quantum mechanics. By unraveling the von Neumann equation for density matrices, we develop a superposition-free formulation of quantum mechanics. Stochastic quantum jumps are a key feature of this approach, in blatant contrast with the continuity of the deterministic Schrödinger equation. We explain how quantum entanglement arises. Our superposition-free formulation results offers a new perspective on quantum mechanics.
Equilibration and the eigenstate thermalization hypothesis as limits to observing macroscopic quantum superpositions
Escola Politécnica de Pernambuco, Universidade de Pernambuco（伯南布哥联邦大学应用理工学院）；Universidade Estadual de Santa Cruz（圣克鲁斯州立大学）；Instituto de Física, Universidade Federal Fluminense（弗鲁米嫩塞联邦大学物理研究所）
In this paper, we propose a feasible scheme for generating the Schrödinger cat states of a macroscopic mechanical resonator in pulsed cavity optomechanics. Starting with cooling the mechanical oscillator to its ground state, a red and a blue pulses with different powers are simultaneously employed to drive the cavity to achieve squeezed mechanical states. Subsequently, a second red pulse is utilized to generate the macroscopic mechanical quantum superpositions, conditioned on the detection of cavity output photons. Finally, after being stored in the resonator for a period of time, the mechanic…
We propose a simple scheme to generate deterministic entanglement between two movable end mirrors in a Fabry-Perot cavity using a single photon superposition state. We derive analytically the expressions of the generated entangled states and the degree of entanglement for each state. We show that strong entanglement can be obtained either in the single-photon strong coupling regime deterministically or in the single-photon weak coupling regime conditionally.
