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arXiv:1105.1856 · Physical Review A

Quantum-measurement backaction from a Bose-Einstein condensate coupled to a mechanical oscillator

Steven Steinke, Swati Singh, Mehmet Emre Taşgın, Pierre Meystre, Keith Schwab, Mukund Vengalattore

Published Aug 25, 2011• 23 citations
arXivHTMLPDF

Abstract

We study theoretically the dynamics of a hybrid optomechanical system consisting of a macroscopic mechanical membrane magnetically coupled to a spinor Bose-Einstein condensate via a nanomagnet attached at the membrane center. We demonstrate that this coupling permits us to monitor indirectly the center-of-mass position of the membrane via measurements of the spin of the condensed atoms. These measurements normally induce a significant backaction on the membrane motion, which we quantify for the cases of thermal and coherent initial states of the membrane. We discuss the possibility of measuring this quantum backaction via repeated measurements. We also investigate the potential to generate nonclassical states of the membrane, in particular Schr\"odinger-cat states, via such repeated measurements.

DOI
10.1103/physreva.84.023841

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We study theoretically the dynamics of a hybrid optomechanical system consisting of a macroscopic mechanical membrane magnetically coupled to a spinor Bose-Einstein condensate via a nanomagnet attached at the membrane center. We demonstrate that this coupling permits us to monitor indirectly the center-of-mass position of the membrane via measurements of the spin of the condensed atoms. These measurements normally induce a significant backaction on the membrane motion, which we quantify for the cases of thermal and coherent initial states of the membrane. We discuss the possibility of measuring this quantum backaction via repeated measurements. We also investigate the potential to generate nonclassical states of the membrane, in particular Schr"odinger-cat states, via such repeated measurements.
We theoretically study the coupling of Bose-Einstein condensed atoms to the mechanical oscillations of a nanoscale cantilever with a magnetic tip. This is an experimentally viable hybrid quantum system which allows one to explore the interface of quantum optics and condensed matter physics. We propose an experiment where easily detectable atomic spin flips are induced by the cantilever motion. This can be used to probe thermal oscillations of the cantilever with the atoms. At low cantilever temperatures, as realized in recent experiments, the backaction of the atoms onto the cantilever is significant and the system represents a mechanical analog of cavity quantum electrodynamics. With high but realistic cantilever quality factors, the strong coupling regime can be reached, either with single atoms or collectively with Bose-Einstein condensates. We discuss an implementation on an atom chip.
In this thesis I present experiments investigating controlled coupling between mechanical oscillators and ultracold atoms. I report on three different coupling mechanisms. In a first experiment, the surface potential experienced by atoms close to the mechanical oscillator is employed to couple the oscillator motion to the center of mass (COM) motion of a trapped Bose-Einstein condensate (BEC). The magnetic trapping potential is modified by the surface potential arising from the oscillator surface which results in a reduced trap depth. Vibration of the oscillator leads to a modulation of the trap frequency and the minimum of the trapping potential. Observing the loss of atoms from the BEC allows us to read out the amplitude of the mechanical oscillator with the atoms. In a second experiment, we study the coupling of a mechanical membrane oscillator and thermal atoms trapped in a 1D optical lattice. The membrane is the end mirror of the lattice, and oscillation of the membrane couples to the COM mode of the atomic ensemble. Conversely, the center of mass motion of the atomic ensemble redistributes photons between the two running waves forming the 1D optical lattice, effectively modulating their power, and hence the radiation pressure acting onto the membrane. We observe the action of the oscillating membrane onto the atoms by detecting the resulting temperature increase of the atomic ensemble in absorption imaging. To observe the backaction of the atoms onto the mechanical oscillator, the mechanical damping is measured in experiments with and without atoms in the lattice, and we measure higher damping in the presence of atoms in agreement with the theoretical predictions. These experiments are the first demonstration of backaction of an atomic system onto a mechanical oscillator. We investigate a third coupling mechanism, where the motion of a mechanical oscillator is coupled to the collective spin of a BEC. The tip of a mechanical oscillator is functionalized with a magnet, which transduces the oscillators' motion into oscillations of the magnetic field. This drives spin-flip transitions of trapped atoms to untrapped motional states. The coupling strength is not limited by the square root of the mass ratio of atoms and oscillator as in the other coupling schemes discussed in this thesis. We investigate this coupling scheme theoretically, and discuss the realization of a nanometer-sized mechanical oscillator with a magnetic island. I report on the status of the fabrication, and propose a simplified fabrication method.
This thesis concentrates on generating and measuring non-classical states of mechanical oscillators by coupling them to atomic and molecular quantum systems. We start with a discussion of what novel physics can be explored by mechanical systems operating in the quantum regime. We then discuss one technique making it a possibility- cavity optomechanics, particularly optomechanical cooling. We investigate the limits of optomechanical cooling and review how the coupling of mechanical oscillators to external heat baths limits the minimum attainable phonon occupation number. As a possible alternative for circumventing clamping losses, we consider an all-optical approach where the mechanical element (in this case, a Bragg mirror) is suspended via optical forces, and discuss some limitations of this approach. We explore several schemes aimed at the generation of quantum states in mechanical oscillators. We consider specifically two examples: one in which the mechanical oscillator is coupled to polar molecules via dipole-dipole interaction, and another where it is magnetically coupled to a Bose condensate. The first example emphasizes that such an interaction can generate parametric squeezing and entanglement. The second scheme demonstrates that the back action of BEC spin measurements can be used to generate quantum states of motion of a mechanical oscillator. We then discuss possible methods for measuring the entire density matrix of a mechanical oscillator. The first method achieves the tomographic reconstruction of the mechanical Wigner function by coupling it simultaneously to a classical optical oscillator and a qubit. The second approach involves a state transfer scheme between momentum excitations of a bose-condensate in a cavity and a moving mirror of the cavity that is entirely mediated by the light field. We conclude with a discussion of the broader implications of this work, and some future research directions.
In this paper, we propose a new theoretical scheme for generating a macroscopic Schrödinger cat state of a mechanical oscillator in a hybrid optomechanical system where a beam of two-level atoms passes through the cavity. In the model under consideration, the cavity field couples to the macroscopic mirror through the optomechanical interaction while it couples to the atom through a generalized Jaynes–Cummings interaction that involves the cavity-mode structure. The motion of the mirror modifies the cavity-mode function and therefore modulates the atom-field interaction, leading to the three-mode atom-field-mirror coupling or, equivalently, polariton-mirror coupling in a dressed picture. This interaction induces a controllable anharmonicity in the energy spectrum of the mechanical oscillator, which provides the possibility of generating a superposition of two time-dependent coherent states of the mechanical oscillator just by performing a conditional measurement on the internal states of the atoms exiting the optomechanical cavity. We also investigate the tripartite atom-field-mirror entanglement, which is controllable by adjusting the parameters of the system. In addition, we explore the effects of the mechanical dissipation and thermal noise on the tripartite quantum correlation in the system as well as the generated mechanical superposition state.
We have realized a hybrid optomechanical system by coupling ultracold atoms to a micromechanical membrane. The atoms are trapped in an optical lattice, which is formed by retroreflection of a laser beam from the membrane surface. In this setup, the lattice laser light mediates an optomechanical coupling between membrane vibrations and atomic center-of-mass motion. We observe both the effect of the membrane vibrations onto the atoms as well as the backaction of the atomic motion onto the membrane. By coupling the membrane to laser-cooled atoms, we engineer the dissipation rate of the membrane. Our observations agree quantitatively with a simple model.
We report a spin-orbit-coupling-induced backaction cooling in an optomechanical system, composed of a spin-orbit-coupled Bose-Einstein condensate trapped in an optical cavity with one movable end mirror, by suppressing heating effects of quantum noises. The collective density excitations of the spin-orbit-coupling-mediated hyperfine states---serving as atomic oscillators equally coupled to the cavity field---trigger strongly driven atomic backaction. We find that the backaction not only revamps low-temperature dynamics of its own but also provides an opportunity to cool the mechanical mirror to its quantum-mechanical ground state. Further, we demonstrate that the strength of spin-orbit coupling also superintends dynamic structure factor and squeezes nonlinear quantum noises, like thermomechanical and photon shot noise, which enhances optomechanical features of the hybrid cavity beyond previous investigations. Our findings are testable in a realistic setup and enhance the functionality of cavity optomechanics with spin-orbit-coupled hyperfine states in the field of quantum optics and quantum computation.