Jürgen Appel

Mesoscopic atomic entanglement for precision measurements beyond the standard quantum limit

Squeezing of quantum fluctuations by means of entanglement is a well-recognized goal in the field of quantum information science and precision measurements. In particular, squeezing the fluctuations via entanglement between 2-level atoms can improve the precision of sensing, clocks, metrology, and spectroscopy. Here, we demonstrate 3.4 dB of metrologically relevant squeezing and entanglement for ≳ 105 cold caesium atoms via a quantum nondemolition (QND) measurement on the atom clock levels. We show that there is an optimal degree of decoherence induced by the quantum measurement which maximizes the generated entanglement. A 2-color QND scheme used in this paper is shown to have a number of advantages for entanglement generation as compared with a single-color QND measurement.

Optical detection of radio waves through a nanomechanical transducer

Low-loss transmission and sensitive recovery of weak radio-frequency and microwave signals is a ubiquitous challenge, crucial in radio astronomy, medical imaging, navigation, and classical and quantum communication. Efficient up-conversion of radio-frequency signals to an optical carrier would enable their transmission through optical fibres instead of through copper wires, drastically reducing losses, and would give access to the set of established quantum optical techniques that are routinely used in quantum-limited signal detection. Research in cavity optomechanics has shown that nanomechanical oscillators can couple strongly to either microwave or optical fields. Here we demonstrate a room-temperature optoelectromechanical transducer with both these functionalities, following a recent proposal using a high-quality nanomembrane. A voltage bias of less than 10 V is sufficient to induce strong coupling between the voltage fluctuations in a radio-frequency resonance circuit and the membrane’s displacement, which is simultaneously coupled to light reflected off its surface. The radio-frequency signals are detected as an optical phase shift with quantum-limited sensitivity. The corresponding half-wave voltage is in the microvolt range, orders of magnitude less than that of standard optical modulators. The noise of the transducer—beyond the measured Johnson noise of the resonant circuit—consists of the quantum noise of light and thermal fluctuations of the membrane, dominating the noise floor in potential applications in radio astronomy and nuclear magnetic imaging. Each of these contributions is inferred to be when balanced by choosing an electromechanical cooperativity of with an optical power of 1 mW. The noise temperature of the membrane is divided by the cooperativity. For the highest observed cooperativity of , this leads to a projected noise temperature of 40 mK and a sensitivity limit of . Our approach to all-optical, ultralow-noise detection of classical electronic signals sets the stage for coherent up-conversion of low-frequency quantum signals to the optical domain.

Entanglement-assisted atomic clock beyond the projection noise limit

We use a quantum non-demolition measurement to generate a spin squeezed state and to create entanglement in a cloud of 105 cold cesium atoms. For the first time we operate an atomic clock improved by spin squeezing beyond the projection noise limit in a proof-of-principle experiment. For a clock-interrogation time of 10 μs, the experiments show an improvement of 1.1 dB in the signal-to-noise ratio, compared to the atomic projection noise limit.

Generation and detection of a sub-Poissonian atom number distribution in a one-dimensional optical lattice.

We demonstrate preparation and detection of an atom number distribution in a one-dimensional atomic lattice with the variance -14  dB below the Poissonian noise level. A mesoscopic ensemble containing a few thousand atoms is trapped in the evanescent field of a nanofiber. The atom number is measured through dual-color homodyne interferometry with a pW-power shot noise limited probe. Strong coupling of the evanescent probe guided by the nanofiber allows for a real-time measurement with a precision of ±8  atoms on an ensemble of some 10(3)  atoms in a one-dimensional trap. The method is very well suited for generating collective atomic entangled or spin-squeezed states via a quantum nondemolition measurement as well as for tomography of exotic atomic states in a one-dimensional lattice.

Coherent Backscattering of Light Off One-Dimensional Atomic Strings.

We present the first experimental realization of coherent Bragg scattering off a one-dimensional system-two strings of atoms strongly coupled to a single photonic mode-realized by trapping atoms in the evanescent field of a tapered optical fiber, which also guides the probe light. We report nearly 12% power reflection from strings containing only about 1000 cesium atoms, an enhancement of 2 orders of magnitude compared to reflection from randomly positioned atoms. This result paves the road towards collective strong coupling in 1D atom-photon systems. Our approach also allows for a straightforward fiber connection between several distant 1D atomic crystals.

Nondestructive Probing of Rabi Oscillations on the Cesium Clock Transition near the Standard Quantum Limit

We report on the nondestructive observation of Rabi oscillations on the Cs clock transition. The internal atomic state evolution of a dipole-trapped ensemble of cold atoms is inferred from the phase shift of a probe laser beam as measured using a Mach-Zehnder interferometer. We describe a single color as well as a two-color probing scheme. Using the latter, measurements of the collective pseudospin projection of atoms in a superposition of the clock states are performed and the observed spin fluctuations are shown to be close to the standard quantum limit.

Quantum interference of a single spin excitation with a macroscopic atomic ensemble

We report on the observation of quantum interference of a collective single spin excitation with a spin ensemble of

Inhomogeneous light shift effects on atomic quantum state evolution in non-destructive measurements

N_{\text{atom}} =10^5

Toward quantum state tomography of a single polariton state of an atomic ensemble

atoms. Detection of a single photon scattered from the atoms creates the single spin excitation, a Fock state embedded in the collective spin of the ensemble. The state of the atomic ensemble is then detected by tomography via a quantum non-demolition measurement of the collective spin. A macroscopic difference of the order of

Atomic nonclassicality quasiprobabilities

\sqrt{N_{\text{atom}}}