Monitoring and active stabilization of laser injection locking using beam ellipticity.

We unveil a powerful method for the stabilization of laser injection locking based on sensing variations in the output beam ellipticity of an optically seeded laser. The effect arises due to an interference between the seeding beam and the injected laser output. We demonstrate the method for a commercial semiconductor laser without the need for any internal changes to the readily operational injection locked laser system that was used. The method can also be used to increase the mode-hop free tuning range of lasers, and has the potential to fill a void in the low-noise laser industry.

Analog stabilization of an electro-optic I/Q modulator with an auxiliary modulation tone.

Proper operation of electro-optic I/Q modulators relies on precise adjustment and control of the relative phase biases between the modulator's internal interferometer arms. We present an all-analog phase bias locking scheme where error signals are obtained from the beat between the optical carrier and optical tones generated by an auxiliary 2 MHz R F tone to lock the phases of all three involved interferometers for operation up to 10 GHz. With the developed method, we demonstrate an I/Q modulator in carrier-suppressed single-sideband mode, where the suppressed carrier and sideband are locked at optical power levels <-27d B relative to the transmitted sideband. We describe a simple analytical model for calculating the error signals and detail the implementation of the electronic circuitry for the implementation of the method.

Free Space Ramsey Spectroscopy in Rubidium with Noise below the Quantum Projection Limit.

We demonstrate the utility of optical cavity generated spin-squeezed states in free space atomic fountain clocks in ensembles of 390 000 ^{87}Rb atoms. Fluorescence imaging, correlated to an initial quantum nondemolition measurement, is used for population spectroscopy after the atoms are released from a confining lattice. For a free fall time of 4 milliseconds, we resolve a single-shot phase sensitivity of 814(61) microradians, which is 5.8(0.6) decibels (dB) below the quantum projection limit. We observe that this squeezing is preserved as the cloud expands to a roughly 200 µm radius and falls roughly 300 µm in free space. Ramsey spectroscopy with 240 000 atoms at a 3.6 ms Ramsey time results in a single-shot fractional frequency stability of 8.4(0.2)×10^{-12}, 3.8(0.2) dB below the quantum projection limit. The sensitivity and stability are limited by the technical noise in the fluorescence detection protocol and the microwave system, respectively.

Bell Correlations in Spin-Squeezed States of 500 000 Atoms.

Bell correlations, indicating nonlocality in composite quantum systems, were until recently only seen in small systems. Here, we demonstrate Bell correlations in squeezed states of 5×10^{5} ^{87}Rb atoms. The correlations are inferred using collective measurements as witnesses and are statistically significant to 124 standard deviations. The states are both generated and characterized using optical-cavity aided measurements.

Measurement noise 100 times lower than the quantum-projection limit using entangled atoms.

Quantum metrology uses quantum entanglement--correlations in the properties of microscopic systems--to improve the statistical precision of physical measurements. When measuring a signal, such as the phase shift of a light beam or an atomic state, a prominent limitation to achievable precision arises from the noise associated with the counting of uncorrelated probe particles. This noise, commonly referred to as shot noise or projection noise, gives rise to the standard quantum limit (SQL) to phase resolution. However, it can be mitigated down to the fundamental Heisenberg limit by entangling the probe particles. Despite considerable experimental progress in a variety of physical systems, a question that persists is whether these methods can achieve performance levels that compare favourably with optimized conventional (non-entangled) systems. Here we demonstrate an approach that achieves unprecedented levels of metrological improvement using half a million (87)Rb atoms in their 'clock' states. The ensemble is 20.1 ± 0.3 decibels (100-fold) spin-squeezed via an optical-cavity-based measurement. We directly resolve small microwave-induced rotations 18.5 ± 0.3 decibels (70-fold) beyond the SQL. The single-shot phase resolution of 147 microradians achieved by the apparatus is better than that achieved by the best engineered cold atom sensors despite lower atom numbers. We infer entanglement of more than 680 ± 35 particles in the atomic ensemble. Applications include atomic clocks, inertial sensors, and fundamental physics experiments such as tests of general relativity or searches for electron electric dipole moment. To this end, we demonstrate an atomic clock measurement with a quantum enhancement of 10.5 ± 0.3 decibels (11-fold), limited by the phase noise of our microwave source.

Many-atom-cavity QED system with homogeneous atom-cavity coupling.

We demonstrate a many-atom-cavity system with a high-finesse dual-wavelength standing wave cavity in which all participating rubidium atoms are nearly identically coupled to a 780-nm cavity mode. This homogeneous coupling is enforced by a one-dimensional optical lattice formed by the field of a 1560-nm cavity mode.

Adjustable and robust methods for polarization-dependent focusing.

We present two methods for the precise independent focusing of orthogonal linear polarizations of light at arbitrary relative locations. Our first scheme uses a displaced lens in a polarization Sagnac interferometer to provide adjustable longitudinal and lateral focal displacements via simple geometry; the second uses uniaxial crystals to achieve the same effect in a compact collinear setup. We develop the theoretical applications and limitations of our schemes, and provide experimental confirmation of our calculations.

Raman lasing with a cold atom gain medium in a high-finesse optical cavity.

We demonstrate a Raman laser using cold (87)Rb atoms as the gain medium in a high-finesse optical cavity. We observe robust continuous wave lasing in the atypical regime where single atoms can considerably affect the cavity field. Consequently, we discover unusual lasing threshold behavior in the system causing jumps in lasing power, and propose a model to explain the effect. We also measure the intermode laser linewidth, and observe values as low as 80 Hz. The tunable gain properties of this laser suggest multiple directions for future research.

Observation of the spin hall effect of light via weak measurements.

We have detected a spin-dependent displacement perpendicular to the refractive index gradient for photons passing through an air-glass interface. The effect is the photonic version of the spin Hall effect in electronic systems, indicating the universality of the effect for particles of different nature. Treating the effect as a weak measurement of the spin projection of the photons, we used a preselection and postselection technique on the spin state to enhance the original displacement by nearly four orders of magnitude, attaining sensitivity to displacements of approximately 1 angstrom. The spin Hall effect can be used for manipulating photonic angular momentum states, and the measurement technique holds promise for precision metrology.

Counterfactual quantum computation through quantum interrogation.

The logic underlying the coherent nature of quantum information processing often deviates from intuitive reasoning, leading to surprising effects. Counterfactual computation constitutes a striking example: the potential outcome of a quantum computation can be inferred, even if the computer is not run. Relying on similar arguments to interaction-free measurements (or quantum interrogation), counterfactual computation is accomplished by putting the computer in a superposition of 'running' and 'not running' states, and then interfering the two histories. Conditional on the as-yet-unknown outcome of the computation, it is sometimes possible to counterfactually infer information about the solution. Here we demonstrate counterfactual computation, implementing Grover's search algorithm with an all-optical approach. It was believed that the overall probability of such counterfactual inference is intrinsically limited, so that it could not perform better on average than random guesses. However, using a novel 'chained' version of the quantum Zeno effect, we show how to boost the counterfactual inference probability to unity, thereby beating the random guessing limit. Our methods are general and apply to any physical system, as illustrated by a discussion of trapped-ion systems. Finally, we briefly show that, in certain circumstances, counterfactual computation can eliminate errors induced by decoherence.