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Iranian Journal of Physics Research

Generating macroscopic superposition states by adiabatic transition

Aslani, Mahdi, Abdi, Mehdi

Published Mar 1, 2023• 1 citation
Publisher

Abstract

Since the establishment of the quantum mechanics, researchers in physics have been studying superposition states and especially proposing setups for generating macroscopic objects in a quantum superposition state. Such states are important and of interest both from a foundational perspective and for their applications in the emerging quantum technologies. Here, we propose a circuit quantum electrodynamical setup and an adiabatic scheme for preparing a macroscopic and massive object in a quantum superposition state. The scheme is based on establishing a spatial double-well potential for a macroscopic object and preparing it in the ground state of the potential via an adiabatic transition. The resulting state is a spatial superposition state where the object assumes a superposition of bulked to two opposite directions, e.g. right and left. By numerical solving of the quantum optical master equation and including the environmental effects, we show that the target cat state is achievable with a high fidelity provided the process satisfies the adiabaticity conditions.

DOI
10.47176/ijpr.22.4.01586

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Since the establishment of the quantum mechanics, researchers in physics have been studying superposition states and especially proposing setups for generating macroscopic objects in a quantum superposition state. Such states are important and of interest both from a foundational perspective and for their applications in the emerging quantum technologies. Here, we propose a circuit quantum electrodynamical setup and an adiabatic scheme for preparing a macroscopic and massive object in a quantum superposition state. The scheme is based on establishing a spatial double-well potential for a macroscopic object and preparing it in the ground state of the potential via an adiabatic transition. The resulting state is a spatial superposition state where the object assumes a superposition of bulked to two opposite directions, e.g. right and left. By numerical solving of the quantum optical master equation and including the environmental effects, we show that the target cat state is achievable with a high fidelity provided the process satisfies the adiabaticity conditions.
A shortcut to an adiabatic scheme is proposed for preparing a massive object in a macroscopic spatial superposition state. In this scheme we propose to employ counterdiabatic driving to maintain the system in the ground state of its instantaneous Hamiltonian while the trap potential is tuned from a parabola to a double well. This, in turn, is performed by properly ramping a control parameter. We show that a few counterdiabatic drives are enough for most practical cases. A hybrid electromechanical setup in superconducting circuits is proposed for the implementation. The efficiency of our scheme is benchmarked by numerically solving the system dynamics in the presence of noises and imperfections. The results show that a mechanical resonator with very-high-fidelity spatially distinguishable cat states can be prepared with our protocol. Furthermore, the protocol is robust against noises and imperfections. We also discuss a method for verifying the final state via spectroscopy of a coupled circuit electrodynamical cavity mode. Our work can serve as the ground work to feasibly realize and verify macroscopic superposition states in future experiments. Published by the American Physical Society 2024
The transition from quantum to classical physics remains an intensely debated question even though it has been investigated for more than a century. Further clarifications could be obtained by preparing macroscopic objects in spatial quantum superpositions and proposals for generating such states for nanomechanical devices either in a transient or a probabilistic fashion have been put forward. Here, we introduce a method to deterministically obtain spatial superpositions of arbitrary lifetime via dissipative state preparation. In our approach, we engineer a double-well potential for the motion of the mechanical element and drive it towards the ground state, which shows the desired spatial superposition, via optomechanical sideband cooling. We propose a specific implementation based on a superconducting circuit coupled to the mechanical motion of a lithium-decorated monolayer graphene sheet, introduce a method to verify the mechanical state by coupling it to a superconducting qubit, and discuss its prospects for testing collapse models for the quantum to classical transition.
Macroscopic quantum superpositions of massive objects are very interesting as they have several potential applications, ranging from the exploration of the interaction of gravity with quantum mechanics to quantum sensing. In this article, we propose two related schemes to prepare a spatial superposition of massive quantum oscillator systems with a high Q factor via a superposition of magnetic forces. In the first method, we propose a large spatial superposition of a levitated spherical magnet generated via magnetic forces applied by adjacent flux qubits. We find that in this method the spatial superposition extent Δ z is independent of the size of the particle. In the second method, we propose a large spatial superposition of a magnetically levitated flux qubit, generated via our driving the levitated qubit inductively. In both schemes, we show that ultralarge superpositions Δ z / δ z ZPM ∼ 10 4 – 10 6 are possible, where δ z ZPM is the zero-point motional extent.
Macroscopic superposition states enable fundamental tests of quantum mechanics and hold a huge potential in metrology, sensing, and other quantum technologies. We propose to generate macroscopic superposition states of a large number of atoms in the ground state of a spin-1 Bose-Einstein condensate. Measuring the number of particles in one mode prepares with large probability highly entangled macroscopic superposition states in the two remaining modes. The macroscopic superposition states are heralded by the measurement outcome. Our protocol is robust under realistic conditions in current experiments, including finite adiabaticity, particle loss, and measurement uncertainty.
Quantum entanglement and quantum superposition are fundamental properties of quantum mechanics, which underline quantum information and quantum computation. Preparing quantum states in the macroscopic level is both conceptually interesting for extending quantum physics to a broader sense and fundamentally important for testing the validity of quantum mechanics. In this dissertation, schemes of preparing macroscopic entanglement and macroscopic superposition states in cavity optomechanics are studied using the unitary evolution method in the nonlinear regime or Lyapunov equation in the linearized regime. Quantum entanglement and quantum superposition states can be realized using experimentally feasible parameters with the proposals in this dissertation.\nFirstly, a scheme of entangling two movable end mirrors in a Fabry-Perot cavity that are coupled to a common single photon superposition state is studied. It is shown that strong entanglement can be obtained either in the single-photon strong coupling regime deterministically or in the single-photon weak coupling regime conditionally.\nSecondly, a scheme of entangling two movable end mirrors, that are coupled to two-mode entangled fields generated from a correlated-emission laser is investigated. By tuning the input driving laser frequencies at the Stokes sidebands of the cavity, the radiation-pressure coupling can be linearized as an effective beam-splitter-like interaction. Hence entanglement can be transferred from the two-mode fields to the two mechanical mirrors. Macroscopic entanglement between macroscopic mirrors persists at temperature ~ 1K.\nThirdly, a scheme of creating macroscopic quantum superpositions of a mechanical mirror via periodically flipping a photonic qubit is proposed. Quantum superposition states of a mechanical mirror can be obtained via the nonlinear radiation coupling with a single-photon superposition state. However, the difference between two superposed mechanical states is very small due to the weak single-photon coupling rate available in experiment. By periodically flipping the photonic qubit state, the difference can be magnified. It is shown in detail that this scheme is experimentally feasible under current technology.
Quantum behaviour appears to be lost in macroscopic objects. They do not, for example, form superpositions. In this paper I present two schemes that produce multiparticle superpositions of superfluid flow. By studying the effect of external parameters on the superposition, I have found three conditions that must be satisfied for a superposition to form. The energy of the superposition states must be close, there must be a coupling path between the states and other states must not couple strongly. By optimising these conditions, it may be possible to make Schrödinger cat states, useful for metrology and stable qubits.