Squeezing light with optomechanical and spin-light quantum interfaces
Gian-Luca Schmid, Manel Bosch Aguilera, Chun Tat Ngai, Maryse Ernzer, Luiz Couto Corrêa Pinto Filho, Dennis Høj, Ulrik L. Andersen, Florian Goschin, Philipp Treutlein
We investigate squeezing of light through quantum-noise-limited interactions with two different material systems: an ultracold atomic spin ensemble and a micromechanical membrane. Both systems feature a light-matter quantum interface that we exploit, respectively, to generate polarization squeezing of light through Faraday interaction with the collective atomic spin precession, and ponderomotive quadrature squeezing of light through radiation pressure interaction with the membrane vibrations in an optical cavity. Both experiments are described in a common theoretical framework, highlighting the conceptual similarities between them. The observation of squeezing certifies light-matter coupling with large quantum cooperativity, a prerequisite for applications in quantum science and technology. In our experiments, we obtain a maximal cooperativity of C qu = 10 for the spin and C qu = 9 for the membrane. In particular, our results pave the way for hybrid quantum systems where spin and mechanical degrees of freedom are coherently coupled via light, enabling new protocols for quantum state transfer and entanglement generation over macroscopic distances.
We investigate squeezing of light through quantum-noise-limited interactions with two different material systems: an ultracold atomic spin ensemble and a micromechanical membrane. Both systems feature a light-matter quantum interface that we exploit, respectively, to generate polarization squeezing of light through Faraday interaction with the collective atomic spin precession, and ponderomotive quadrature squeezing of light through radiation pressure interaction with the membrane vibrations in an optical cavity. Both experiments are described in a common theoretical framework, highlighting the conceptual similarities between them. The observation of squeezing certifies light-matter coupling with large quantum cooperativity, a prerequisite for applications in quantum science and technology. In our experiments, we obtain a maximal cooperativity of C qu = 10 for the spin and C qu = 9 for the membrane. In particular, our results pave the way for hybrid quantum systems where spin and mechanical degrees of freedom are coherently coupled via light, enabling new protocols for quantum state transfer and entanglement generation over macroscopic distances.
This thesis presents theoretical and experimental work on light-mediated coupling between a collective atomic spin and a micromechanical membrane oscillator. With our work we address a fundamental question of quantum optics: Can a beam of light mediate coherent Hamiltonian interactions between two distant quantum systems? This is an intriguing question whose answer is not a priori clear, since the light carries away information about the systems and might be subject to losses, giving rise to intrinsic decoherence channels associated with the coupling. Our answer is affirmative and we derive a particularly simple sufficient condition for the interactions to be Hamiltonian: The light field needs to interact twice with the systems and the second interaction has to be the time reversal of the first. We demonstrate theoretically that, even in the presence of significant optical loss, coherent interactions can be realized and generate substantial amounts of entanglement between the systems. \n \nIn our experiments, we employ this approach to strongly couple a spin-polarized atomic ensemble and a micromechanical oscillator via a free-space laser beam across a distance of one meter in a room-temperature environment. The atomic ensemble consists of about ten million laser-cooled Rubidium atoms in an optical dipole trap that interact with the coupling laser via an off-resonant Faraday interaction. The mechanical oscillator is a silicon nitride membrane which is mounted in a single-sided optical cavity and couples to the laser field via radiation-pressure forces. In order to mediate a bidirectional Hamiltonian interaction between spin and membrane, the coupling beam is arranged in a loop such that it couples twice to the spin. This looped geometry enables destructive interference of quantum back-action by the light field on the spin. \n \nUsing this setup, we experimentally demonstrate for the first time strong Hamiltonian coupling between remote quantum systems and explore different dynamical regimes of cascaded light-mediated interactions: With the spin initialized in its ground state we observe normal-mode splitting and coherent energy exchange oscillations, both hallmarks of strong coupling. If we invert the spin to its highest energy state, we observe parametric-gain interactions, resulting in two-mode thermal noise squeezing. Furthermore, by shifting the phase of the light field between spin and membrane we can switch to non-Hamiltonian coupled dynamics, allowing us to observe level attraction and exceptional points. This high level of control in a strongly coupled modular system gives access to a unique toolbox for designing hybrid quantum systems and coherent optical feedback loops. Our approach to engineer coherent long-distance interactions with light makes it possible to couple very different systems in a modular way, opening up a range of new opportunities for quantum control. \n
We experimentally demonstrate a source of squeezed light featuring simultaneous ponderomotive squeezing from two mechanical modes of an optomechanical system. We use ultra-coherent vibrational modes (Q factors on the order of 108) of a soft-clamped membrane placed in a Fabry–Pérot optical cavity at cryogenic conditions (T=11K) to create correlations between amplitude and phase quadratures of the light field. As a result of the interaction between the membrane position and the light, we generated ponderomotive squeezing of 4.8dB for the first localized mechanical mode at 1.32MHz and 4.2dB for the second localized mode at 2.43MHz, as observed in direct detection when correcting for the detection inefficiency. Thus, we have demonstrated that by leveraging more than one quantum-limited mechanical mode, optomechanical squeezed light generation can be extended to dual-band operation with an ample band separation of about an octave. Utilizing homodyne detection to detect squeezing in an optimal quadrature would lead to squeezing levels at the output of the cavity of 7.3 dB and 6.8 dB, in the two modes, respectively. Squeezing of light demonstrated here for near-infrared light can be achieved in a broad range of wavelengths due to the relative insensitivity of optomechanical interaction with SiN membranes to the wavelength. The demonstrated dual-band squeezing can be linked to the generation of two photon–phonon entangled mode pairs, suggesting that our system, viewed as an entanglement source, is more resource-efficient than single-mode optomechanics.
Quantum entanglement and squeezing associated with the motions of massive mechanical oscillators play an essential role in both fundamental science and emerging quantum technologies, yet realizing such macroscopic nonclassical states remains a formidable challenge. In this paper, we investigate how to achieve strong optomechanical entanglement and mechanical squeezing in a membrane-embedded cavity optomechanical system incorporating a coherent feedback loop, where the membrane interacts with the cavity mode through both linear and quadratic optomechanical couplings. This hybrid optomechanical architecture offers a flexible tunability of intrinsic system parameters, thereby enabling controlled stiffening or softening of the mechanical mode through adjusting quadratic optomechanical coupling, as well as effective modulation of the cavity decay rate via feedback control. More importantly, the synergistic interplay effect allows for a strategic reconfiguration of the system's stability regime, which in turn permits the presence of significantly enhanced effective optomechanical coupling strengths before entering the unstable regime. Exploiting these unique features, we demonstrate that optomechanical entanglement can be substantially enhanced with positive coupling sign and suitable feedback parameters, while strong mechanical squeezing beyond the 3dB limit is simultaneously achieved over a broad parameter range with negative coupling sign, reaching squeezing degree above 10dB under optimized conditions. Our proposal, establishing an all-optical method for generating highly entangled or squeezed states in cavity optomechanical systems, opens up a new route to explore macroscopic quantum effects and to advance quantum information processing.
We report on the realization of a hybrid optomechanical system in which ultracold atoms are coupled to a micromechanical membrane. The atoms are trapped in the intensity maxima of an optical standing wave formed by retroreflection of a laser beam from the membrane surface. Vibrations of the membrane displace the standing wave, thus coupling to the center-of-mass motion of the atomic ensemble. Conversely, atoms imprint their motion onto the laser light, thereby modulating the radiation pressure force on the membrane. In this way, the laser light mediates a long-distance coherent coupling between the two systems. When the trap frequency of the atoms is matched to the membrane frequency, we observe resonant energy transfer. Moreover, we demonstrate sympathetic damping of the membrane motion by coupling it to laser-cooled atoms. Theoretical investigations show that the coupling strength can be considerably enhanced by placing the membrane inside an optical cavity. This could lead to quantum coherent coupling and ground-state cooling of the membrane via a distant atomic ensemble.
Quantum entanglement and squeezing associated with the motions of massive mechanical oscillators play an essential role in both fundamental science and emerging quantum technologies, yet realizing such macroscopic nonclassical states remains a formidable challenge. In this paper, we investigate how to achieve strong optomechanical entanglement and mechanical squeezing in a membrane-embedded cavity optomechanical system incorporating a coherent feedback loop, where the membrane interacts with the cavity mode through both linear and quadratic optomechanical couplings. This hybrid optomechanical architecture offers a flexible tunability of intrinsic system parameters, thereby enabling controlled stiffening or softening of the mechanical mode through adjusting quadratic optomechanical coupling, as well as effective modulation of the cavity decay rate via feedback control. More importantly, the synergistic interplay effect allows for a strategic reconfiguration of the system's stability regime, which in turn permits the presence of significantly enhanced effective optomechanical coupling strengths before entering the unstable regime. Exploiting these unique features, we demonstrate that optomechanical entanglement can be substantially enhanced with positive coupling sign and suitable feedback parameters, while strong mechanical squeezing beyond the 3dB limit is simultaneously achieved over a broad parameter range with negative coupling sign, reaching squeezing degree above 10dB under optimized conditions. Our proposal, establishing an all-optical method for generating highly entangled or squeezed states in cavity optomechanical systems, opens up a new route to explore macroscopic quantum effects and to advance quantum information processing.
We study the generation of atomic-squeezed states for a Bose-Einstein Condensate confined within the lossless optomechanical cavity using pondermotively squeezed light. We show that the radiation pressure coupling between the optical cavity field and mechanical motion of the cavity end mirror generates squeezing of light. This radiation pressure induced light squeezing gets transferred to the condensate atoms via Tavis-Cummings type interaction and results in squeezed-spin states. We further discuss the effect of optomechanical coupling on squeezed atomic states.