A two-mode entangled state was generated experimentally through mixing two squeezed lights from two optical parametric amplifiers on a 50/50 beam splitter.The entangled beams were measured by means of two pairs of balanced homodyne detection systems respectively.The relative phases between the local beams and the detected beams can be locked by using the optical phase modulation technique.The covariance matrix of the two-mode entangled state was obtained when the relative phase of the local beam and the detected beam in one homodyne detection system is locked and the other is scanned.This method provides a way by which one can extract the covariance matrix of any selected quadrature components of two-mode Gaussian state.
We report an experimental observation of a record-breaking ultrahigh rotation frequency about 6 GHz in an optically levitated nanoparticle system. We optically trap a nanoparticle in the gravity direction with a high numerical aperture (NA) objective lens,which shows significant advantages in compensating the influences of the scattering force and the photophoretic force on the trap,especially at intermediate pressure (about100 Pa). This allows us to trap a nanoparticle from atmospheric to low pressure (10^(-3)Pa) without using feedback cooling. We measure a highest rotation frequency about 4.3 GHz of the trapped nanoparticle without feedback cooling and a 6 GHz rotation with feedback cooling,which is the fastest mechanical rotation ever reported to date.Our work provides useful guides for efficiently observing hyperfast rotation in the optical levitation system and may find various applications such as in ultra-sensitive torque detection,probing vacuum friction,and testing unconventional decoherence theories.
The squeezed state was experimentally produced in the four wave mixing process for the first time thirty years ago [1]. Its intrinsic nonclassical property has always attracted the attention of the scientists, and it has also presented an unpredictable application potential in quantum information pro- cessing [2-6] and quantum metrology [7-9]. For gaining an insight into the quantum state, Bertrand et al. [10] intro- duced the concept of quantum tomography into quantum mechanics in 1987. And in 1997, Breitenbach et al. [11] pre- sented the noise distribution of the squeezed states of light fields and reconstructed the quantum states by balanced homodyne detection （BHD）. If the squeezed state light field has a relatively strong amplitude, BHD is not suitable. Consequently, other approaches have also been studied, such as self-tomography of the twin-beam state [12] and selftomography of the single-mode squeezed light field with an empty cavity [ 13]. These approaches enable people to understand the nature of the quantum state.
Realizing a large-scale fully controllable quantum system is a challenging task in current physical research and has broad applications.In this work,we create a reconfigurable optically levitated nanoparticle array in vacuum.Our optically levitated nanoparticle array allows full control of individual nanoparticles to form an arbitrary pattern and detect their motion.As a concrete example,we choose two nanoparticles without rotation signals from an array to synthesize a nanodumbbell in situ by merging them into one trap.The nanodumbbell synthesized in situ can rotate beyond 1 GHz.Our work provides a platform for studying macroscopic many-body physics and quantum sensing.
The optically levitated object is intrinsically isolated from the thermal bath compared with the opto-mechanical oscillator connected to the thermal environment via the cantilever [1,2]. Thus the limitation of the thermalization and decoherence in- troduced by the cantilever is cancelled. The Q-factor of the system is predicted to approach 1012 and the system is extremely sensitive to some changes [3-6]. And it is expected to detect non-Newtonian gravity forces at very small scales [7], the impact of single air molecules [8], nanoscaie temperature [9], and magnetic spin resonance [10]. Importantly it can be used to test the fundamental physical problems.
The mode splitting in a system with Doppler-broadened high-density two-level atoms in the presence of magnetic field inside a relatively long optical cavity is studied in the superstrong coupling regime(atoms-cavity coupling strength g√N is near or larger than the cavity free-spectral range?FSR).The effect of a magnetic field applied along the quantization axis is used to break the polarization degeneracy of the cavity and thereby introduce birefringence(or Faraday rotation)into the medium.The cavity modes are further split in the presence of the magnetic field compared with the normal case of the multi-normal-mode splitting of the two-level system near the D2 line of87Rb.The dependence of the mode splitting on the magnetic field and the temperature is studied.The theoretical analysis according to the linear dispersion theory can provide a good explanation.
