Generation of spin squeezing via continuous quantum nondemolition measurement

Concurrent Spin Squeezing and Light Squeezing in an Atomic Ensemble

Squeezed spin states and squeezed light are both key resources for quantum metrology and quantum information science, but have been separately investigated in experiments so far. Simultaneous generation of these two types of quantum states in one experiment setup is intriguing but remains a challenging goal. Here, we propose a novel protocol based on judiciously engineered symmetric atom-light interaction, and report proof-of-principle experimental results of concurrent spin squeezing of 0.61±0.09  dB and light squeezing of 0.65_{-0.10}^{+0.11}  dB in a hot atomic ensemble. The squeezing process is deterministic, yielding fixed squeezing directions for both the light field and the collective atomic spin. Furthermore, the squeezed light modes lie in the multiple frequency sidebands of a single spatial mode. This new type of dual squeezed state is applicable for quantum enhanced metrology and quantum networks. Our method can be extended to other quantum platforms such as optomechanics, cold atoms, and trapped ions.

Universal Control of Symmetric States Using Spin Squeezing

The manipulation of quantum many-body systems is a crucial goal in quantum science. Entangled quantum states that are symmetric under qubits permutation are of growing interest. Yet, the creation and control of symmetric states has remained a challenge. Here, we introduce a method to universally control symmetric states, proposing a scheme that relies solely on coherent rotations and spin squeezing. We present protocols for the creation of different symmetric states including Schrödinger's cat and Gottesman-Kitaev-Preskill states. The obtained symmetric states can be transferred to traveling photonic states via spontaneous emission, providing a powerful approach for engineering desired quantum photonic states.

Heisenberg-limited spin squeezing in a hybrid system with silicon-vacancy centers

In this paper, we investigate the spin squeezing in a hybrid quantum system consisting of a Silicon-Vacancy (SiV) center ensemble coupled to a diamond acoustic waveguide via the strain interaction. Two sets of non-overlapping driving fields, each contains two time-dependent microwave fields, are applied to this hybrid system. By modulating these fields, the one-axis twist (OAT) interaction and two-axis two-spin (TATS) interaction can be independently realized. In the latter case the squeezing parameter scales to spin number as ξ R2∼1.61N -0.64 with the consideration of dissipation, which is very close to the Heisenberg limit. Furthermore, this hybrid system allows for the study of spin squeezing generated by the simultaneous presence of OAT and TATS interactions, which reveals sensitivity to the parity of the number of spins Ntot, whether it is even or odd. Our scheme enriches the approach for generating Heisenberg-limited spin squeezing in spin-phonon hybrid systems and offers the possibility for future applications in quantum information processing.

One- and Two-Axis Squeezing via Laser Coupling in an Atomic Fermi-Hubbard Model

Generation, storage, and utilization of correlated many-body quantum states are crucial objectives of future quantum technologies and metrology. Such states can be generated by the spin-squeezing protocols, i.e., one-axis twisting and two-axis countertwisting. In this Letter, we show activation of these two squeezing mechanisms in a system composed of ultracold atomic fermions in the Mott insulating phase by a position-dependent laser coupling of atomic internal states. Realization of both the squeezing protocols is feasible in the current state-of-the-art experiments.

Generating Stable Spin Squeezing by Squeezed-Reservoir Engineering

As a genuine many-body entanglement, spin squeezing (SS) can be used to realize the highly precise measurement beyond the limit constrained by classical physics. Its generation has attracted much attention recently. It was reported that N two-level systems (TLSs) located near a one-dimensional waveguide can generate SS by using the mediation effect of the waveguide. However, a coherent driving on each TLS is used to stabilize the SS, which raises a high requirement for experiments. We here propose a scheme to generate stable SS resorting to neither the spin-spin coupling nor the coherent driving on the TLSs. Incorporating the mediation role of the common waveguide and the technique of squeezed-reservoir engineering, our scheme exhibits the advantages over previous ones in the scaling relation of the SS parameter with the number of the TLSs. The long-range correlation feature of the generated SS along the waveguide in our scheme may endow it with certain superiority in quantum sensing, e.g., improving the sensing efficiency of spatially unidentified weak magnetic fields.

Detecting an Itinerant Optical Photon Twice without Destroying It

Nondestructive quantum measurements are central for quantum physics applications ranging from quantum sensing to quantum computing and quantum communication. Employing the toolbox of cavity quantum electrodynamics, we here concatenate two identical nondestructive photon detectors to repeatedly detect and track a single photon propagating through a 60 m long optical fiber. By demonstrating that the combined signal-to-noise ratio of the two detectors surpasses each single one by about 2 orders of magnitude, we experimentally verify a key practical benefit of cascaded nondemolition detectors compared to conventional absorbing devices.

Noisy Quantum Metrology Enhanced by Continuous Nondemolition Measurement

We show that continuous quantum nondemolition (QND) measurement of an atomic ensemble is able to improve the precision of frequency estimation even in the presence of independent dephasing acting on each atom. We numerically simulate the dynamics of an ensemble with up to N=150 atoms initially prepared in a (classical) spin coherent state, and we show that, thanks to the spin squeezing dynamically generated by the measurement, the information obtainable from the continuous photocurrent scales superclassically with respect to the number of atoms N. We provide evidence that such superclassical scaling holds for different values of dephasing and monitoring efficiency. We moreover calculate the extra information obtainable via a final strong measurement on the conditional states generated during the dynamics and show that the corresponding ultimate limit is nearly achieved via a projective measurement of the spin-squeezed collective spin operator. We also briefly discuss the difference between our protocol and standard estimation schemes, where the state preparation time is neglected.

Noise-suppressing and lock-free optical interferometer for cold atom experiments

A novel noise-suppressing and lock-free interferometer is proposed and experimentally demonstrated in the study of the quantum non-destructive (QND) interaction of cold atoms. A QND measurement based on far-off resonant dispersive probing is usually carried out by a Mach-Zehnder type interferometer. It is an experimental challenge in its own right to reduce the classical noise, such as acoustic noise, phase noise and amplitude noise of lasers, and to lock the interferometer at the white-light position that corresponds to a nearly zero path-length difference. Here, we report an interferometer with an inserted acousto-optic modulator (AOM). It is noise immune and lock-free in principle. The experiments show that the new interferometer is able to measure cold atoms for more than 30 minutes and reduce the phase noise by about 30 dB.

Simulating Nonlinear Dynamics of Collective Spins via Quantum Measurement and Feedback

We study a method to simulate quantum many-body dynamics of spin ensembles using measurement-based feedback. By performing a weak collective measurement on a large ensemble of two-level quantum systems and applying global rotations conditioned on the measurement outcome, one can simulate the dynamics of a mean-field quantum kicked top, a standard paradigm of quantum chaos. We analytically show that there exists a regime in which individual quantum trajectories adequately recover the classical limit, and show the transition between noisy quantum dynamics to full deterministic chaos described by classical Lyapunov exponents. We also analyze the effects of decoherence, and show that the proposed scheme represents a robust method to explore the emergence of chaos from complex quantum dynamics in a realistic experimental platform based on an atom-light interface.

Long-Lived Entanglement Generation of Nuclear Spins Using Coherent Light

Nuclear spins of noble-gas atoms are exceptionally isolated from the environment and can maintain their quantum properties for hours at room temperature. Here we develop a mechanism for entangling two such distant macroscopic ensembles by using coherent light input. The interaction between the light and the noble-gas spins in each ensemble is mediated by spin-exchange collisions with alkali-metal spins, which are only virtually excited. The relevant conditions for experimental realizations with ^{3}He or ^{129}Xe are outlined.

Adhesion Effect on the Hyperfine Frequency Shift of an Alkali Metal Vapor Cell with Paraffin Coating Using Peak-Force Tapping AFM

We have investigated the adhesion effect on the hyperfine frequency shift of an alkali metal vapor cell with paraffin coating using the peak-force tapping AFM (atomic force microscopy) technique by developing a uniform and high-quality paraffin coating method. We observed a relatively uniform temperature field on the substrate can be obtained theoretically and experimentally with the closed-type previse temperature-controlled evaporation method. The roughness and adhesion of the coating surface as low as 0.8 nm and 20 pN were successfully obtained, respectively. Furthermore, the adhesion information dependence of the topography was investigated from the force spectroscopy, which indicates that the adhesion force jumped on the edge of the particles and stepped but remained constant above the particles and steps regardless of their height for paraffin coating. Finally, we can evaluate the relaxation and the hyperfine frequency shift of an alkali metal vapor cell through accurately calculating the surface adsorption energy of the paraffin coating from peak-force tapping information. This finding is crucial for improving the sensitivity of the atomic sensors through directly analyzing the adhesion effect of the paraffin coating films instead of measuring the relaxation times.

Continuous Real-Time Tracking of a Quantum Phase Below the Standard Quantum Limit

We propose a scheme for continuously measuring the evolving quantum phase of a collective spin composed of N pseudospins. Quantum nondemolition measurements of a lossy cavity mode interacting with an atomic ensemble are used to directly probe the phase of the collective atomic spin without converting it into a population difference. Unlike traditional Ramsey measurement sequences, our scheme allows for real-time tracking of time-varying signals. As a bonus, spin-squeezed states develop naturally, providing real-time phase estimation significantly more precise than the standard quantum limit of Δϕ_{SQL}=1/sqrt[N]  rad.

Enhanced Magnetic Sensitivity with Non-Gaussian Quantum Fluctuations

The precision of a quantum sensor can overcome its classical counterpart when its constituents are entangled. In Gaussian squeezed states, quantum correlations lead to a reduction of the quantum projection noise below the shot noise limit. However, the most sensitive states involve complex non-Gaussian quantum fluctuations, making the required measurement protocol challenging. Here we measure the sensitivity of nonclassical states of the electronic spin J=8 of dysprosium atoms, created using light-induced nonlinear spin coupling. Magnetic sublevel resolution enables us to reach the optimal sensitivity of non-Gaussian (oversqueezed) states, well above the capability of squeezed states and about half the Heisenberg limit.

Measurement-induced dynamics and stabilization of spinor-condensate domain walls

Weakly measuring many-body systems and allowing for feedback in real time can simultaneously create and measure new phenomena in quantum systems. We theoretically study the dynamics of a continuously measured two-component Bose-Einstein condensate (BEC) potentially containing a domain wall and focus on the tradeoff between usable information obtained from measurement and quantum backaction. Each weakly measured system yields a measurement record from which we extract real-time dynamics of the domain wall. We show that quantum backaction due to measurement causes two primary effects: domain-wall diffusion and overall heating. The system dynamics and signal-to-noise ratio depend on the choice of measurement observable. We propose a feedback protocol to dynamically create a stable domain wall in the regime where domain walls are unstable, giving a prototype example of Hamiltonian engineering using measurement and feedback.

Optimization of photon storage fidelity in ordered atomic arrays

A major application for atomic ensembles consists of a quantum memory for light, in which an optical state can be reversibly converted to a collective atomic excitation on demand. There exists a well-known fundamental bound on the storage error, when the ensemble is describable by a continuous medium governed by the Maxwell-Bloch equations. However, these equations are semi-phenomenological, as they treat emission of the atoms into other directions other than the mode of interest as being independent. On the other hand, in systems such as dense, ordered atomic arrays, atoms interact with each other strongly and spatial interference of the emitted light might be exploited to suppress emission into unwanted directions, thereby enabling improved error bounds. Here, we develop a general formalism that fully accounts for spatial interference, and which finds the maximum storage efficiency for a single photon with known spatial input mode into a collection of atoms with discrete, known positions. As an example, we apply this technique to study a finite two-dimensional square array of atoms. We show that such a system enables a storage error that scales with atom number N a like ∼ ( log N a ) 2 ∕ N a 2 , and that, remarkably, an array of just 4 × 4 atoms in principle allows for an error of less than 1%, which is comparable to a disordered ensemble with an optical depth of around 600.

Simultaneous tracking of spin angle and amplitude beyond classical limits

Measurement of spin precession is central to extreme sensing in physics, geophysics, chemistry, nanotechnology and neuroscience, and underlies magnetic resonance spectroscopy. Because there is no spin-angle operator, any measurement of spin precession is necessarily indirect, for example, it may be inferred from spin projectors at different times. Such projectors do not commute, and so quantum measurement back-action-the random change in a quantum state due to measurement-necessarily enters the spin measurement record, introducing errors and limiting sensitivity. Here we show that this disturbance in the spin projector can be reduced below N1/2-the classical limit for N spins-by directing the quantum measurement back-action almost entirely into an unmeasured spin component. This generates a planar squeezed state that, because spins obey non-Heisenberg uncertainty relations, enables simultaneous precise knowledge of spin angle and spin amplitude. We use high-dynamic-range optical quantum non-demolition measurements applied to a precessing magnetic spin ensemble to demonstrate spin tracking with steady-state angular sensitivity 2.9 decibels below the standard quantum limit, simultaneously with amplitude sensitivity 7.0 decibels below the Poissonian variance. The standard quantum limit and Poissonian variance indicate the best possible sensitivity with independent particles. Our method surpasses these limits in non-commuting observables, enabling orders-of-magnitude improvements in sensitivity for state-of-the-art sensing and spectroscopy.

Quantum control of spin-nematic squeezing in a dipolar spin-1 condensate

Versatile controllability of interactions and magnetic field in ultracold atomic gases ha now reached an era where spin mixing dynamics and spin-nematic squeezing can be studied. Recent experiments have realized spin-nematic squeezed vacuum and dynamic stabilization following a quench through a quantum phase transition. Here we propose a scheme for storage of maximal spin-nematic squeezing, with its squeezing angle maintained in a fixed direction, in a dipolar spin-1 condensate by applying a microwave pulse at a time that maximal squeezing occurs. The dynamic stabilization of the system is achieved by manipulating the external periodic microwave pulses. The stability diagram for the range of pulse periods and phase shifts that stabilize the dynamics is numerical simulated and agrees with a stability analysis. Moreover, the stability range coincides well with the spin-nematic vacuum squeezed region which indicates that the spin-nematic squeezed vacuum will never disappear as long as the spin dynamics are stabilized.

Mean-Field Dynamics and Fisher Information in Matter Wave Interferometry

There has been considerable recent interest in the mean-field dynamics of various atom-interferometry schemes designed for precision sensing. In the field of quantum metrology, the standard tools for evaluating metrological sensitivity are the classical and quantum Fisher information. In this Letter, we show how these tools can be adapted to evaluate the sensitivity when the behavior is dominated by mean-field dynamics. As an example, we compare the behavior of four recent theoretical proposals for gyroscopes based on matter-wave interference in toroidally trapped geometries. We show that while the quantum Fisher information increases at different rates for the various schemes considered, in all cases it is consistent with the well-known Sagnac phase shift after the matter waves have traversed a closed path. However, we argue that the relevant metric for quantifying interferometric sensitivity is the classical Fisher information, which can vary considerably between the schemes.

Squeezing and Entanglement of Density Oscillations in a Bose-Einstein Condensate

The dispersive interaction of atoms and a far-detuned light field allows nondestructive imaging of the density oscillations in Bose-Einstein condensates. Starting from a ground state condensate, we investigate how the measurement backaction leads to squeezing and entanglement of the quantized density oscillations. We show that properly timed, stroboscopic imaging and feedback can be used to selectively address specific eigenmodes and avoid excitation of nontargeted modes of the system.

Alkali-Metal Spin Maser

Quantum measurement is a combination of a read-out and a perturbation of the quantum system. We explore the nonlinear spin dynamics generated by a linearly polarized probe beam in a continuous measurement of the collective spin state in a thermal alkali-metal atomic sample. We demonstrate that the probe-beam-driven perturbation leads, in the presence of indirect pumping, to complete polarization of the sample and macroscopic coherent spin oscillations. As a consequence of the former we report observation of spectral profiles free from collisional broadening. Nonlinear dynamics is studied through exploring its effect on radio frequency as well as spin noise spectra.

Spin squeezing in a quadrupolar nuclei NMR system

We have produced and characterized spin-squeezed states at a temperature of 26 °C in a nuclear magnetic resonance quadrupolar system. The experiment was carried out on 133Cs nuclei of spin I=7/2 in a sample of lyotropic liquid crystal. The source of spin squeezing was identified as the interaction between the quadrupole moment of the nuclei and the electric field gradients present within the molecules. We use the spin angular momentum representation to describe formally the nonlinear operators that produce the spin squeezing on a Hilbert space of dimension 2I+1=8. The quantitative and qualitative characterization of this spin-squeezing phenomenon is expressed by a squeezing parameter and squeezing angle developed for the two-mode Bose-Einstein condensate system, as well as by the Wigner quasiprobability distribution function. The generality of the present experimental scheme points to potential applications in solid-state physics.

Spin squeezing in a Rydberg lattice clock

We theoretically demonstrate a viable approach to spin squeezing in optical lattice clocks via optical dressing of one clock state to a highly excited Rydberg state, generating switchable atomic interactions. For realistic experimental parameters, these interactions are shown to generate over 10 dB of squeezing in large ensembles within a few microseconds and without degrading the subsequent clock interrogation.

Observing single quantum trajectories of a superconducting quantum bit

The length of time that a quantum system can exist in a superposition state is determined by how strongly it interacts with its environment. This interaction entangles the quantum state with the inherent fluctuations of the environment. If these fluctuations are not measured, the environment can be viewed as a source of noise, causing random evolution of the quantum system from an initially pure state into a statistical mixture--a process known as decoherence. However, by accurately measuring the environment in real time, the quantum system can be maintained in a pure state and its time evolution described by a 'quantum trajectory' determined by the measurement outcome. Here we use weak measurements to monitor a microwave cavity containing a superconducting quantum bit (qubit), and track the individual quantum trajectories of the system. In this set-up, the environment is dominated by the fluctuations of a single electromagnetic mode of the cavity. Using a near-quantum-limited parametric amplifier, we selectively measure either the phase or the amplitude of the cavity field, and thereby confine trajectories to either the equator or a meridian of the Bloch sphere. We perform quantum state tomography at discrete times along the trajectory to verify that we have faithfully tracked the state of the quantum system as it diffuses on the surface of the Bloch sphere. Our results demonstrate that decoherence can be mitigated by environmental monitoring, and validate the foundation of quantum feedback approaches based on Bayesian statistics. Moreover, our experiments suggest a new means of implementing 'quantum steering'--the harnessing of action at a distance to manipulate quantum states through measurement.

Near-Heisenberg-limited atomic clocks in the presence of decoherence

The ultimate stability of atomic clocks is limited by the quantum noise of the atoms. To reduce this noise it has been suggested to use entangled atomic ensembles with reduced atomic noise. Potentially this can push the stability all the way to the limit allowed by the Heisenberg uncertainty relation, which is denoted the Heisenberg limit. In practice, however, entangled states are often more prone to decoherence, which may prevent reaching this performance. Here we present an adaptive measurement protocol that in the presence of a realistic source of decoherence enables us to get near-Heisenberg-limited stability of atomic clocks using entangled atoms. The protocol may thus realize the full potential of entanglement for quantum metrology despite the detrimental influence of decoherence.

Optical pump-probe detection of manganese hyperfine beats in (Cd,Mn)Te crystals

Optical pump-probe experiments reveal spin beats of manganese ions in (Cd,Mn)Te, due to hyperfine and crystal fields. At "magic" orientations of the magnetic field, the effect of local crystal field is strongly suppressed. In this case, the spin precession of Mn(2+) embedded in the lattice approaches the precession expected for the free ion. Following optical excitation, regular spin pulses show up, revealing the one-to-one correspondence between precession frequency and Mn(2+) nuclear spin state. The period of the spin pulses accurately determines the hyperfine constant |A|=705  neV. The manganese spin coherence time up to T(2)(Mn)≃15  ns is measured for a manganese concentration x=0.0011.

Quantum collapse and the second law of thermodynamics

A heat engine undergoes a cyclic operation while in equilibrium with the net result of conversion of heat into work. Quantum effects such as superposition of states can improve an engine's efficiency by breaking detailed balance, but this improvement comes at a cost due to excess entropy generated from collapse of superpositions on measurement. We quantify these competing facets for a quantum ratchet composed of an ensemble of pairs of interacting two-level atoms. We suggest that the measurement postulate of quantum mechanics is intricately connected to the second law of thermodynamics. More precisely, if quantum collapse is not inherently random, then the second law of thermodynamics can be violated. Our results challenge the conventional approach of simply quantifying quantum correlations as a thermodynamic work deficit.

Enhanced temperature sensitivity in vapor-cell frequency standards

We report on the measurement of an anomalously large temperature sensitivity of the clock frequency in a Rb cell with buffer gas. The effect is observed in a prototype of pulsed optically pumped frequency standard which allows high resolution measurements because of its frequency stability at the level 1.7 × 10(-13) for 1 s of measurement time. We attribute this phenomenon to the geometry of the interaction and to the presence in the cell of temperature inhomogeneities that may enhance the temperature sensitivity of the clock frequency via the buffer gas pressure coefficient. We also propose some solutions to reduce this unwanted effect that may limit the medium-long-term performances of high-frequency-stability vapor-cell clocks.

Enhanced squeezing of a collective spin via control of its qudit subsystems

Unitary control of qudits can improve the collective spin squeezing of an atomic ensemble. Preparing the atoms in a state with large quantum fluctuations in magnetization strengthens the entangling Faraday interaction. The resulting increase in interatomic entanglement can be converted into metrologically useful spin squeezing. Further control can squeeze the internal atomic spin without compromising entanglement, providing an overall multiplicative factor in the collective squeezing. We model the effects of optical pumping and study the tradeoffs between enhanced entanglement and decoherence. For realistic parameters we see improvements of ~10 dB.

Pulsed quantum optomechanics

Studying mechanical resonators via radiation pressure offers a rich avenue for the exploration of quantum mechanical behavior in a macroscopic regime. However, quantum state preparation and especially quantum state reconstruction of mechanical oscillators remains a significant challenge. Here we propose a scheme to realize quantum state tomography, squeezing, and state purification of a mechanical resonator using short optical pulses. The scheme presented allows observation of mechanical quantum features despite preparation from a thermal state and is shown to be experimentally feasible using optical microcavities. Our framework thus provides a promising means to explore the quantum nature of massive mechanical oscillators and can be applied to other systems such as trapped ions.

Limit of spin squeezing in finite-temperature Bose-Einstein condensates

We show that, at finite temperature, the maximum spin squeezing achievable using interactions in Bose-Einstein condensates has a finite limit when the atom number N→∞ at fixed density and interaction strength. We calculate the limit of the squeezing parameter for a spatially homogeneous system and show that it is bounded from above by the initial noncondensed fraction.

Spin squeezing: transforming one-axis twisting into two-axis twisting

Squeezed spin states possess unique quantum correlation or entanglement and are significantly promising for advancing quantum information processing and quantum metrology. In recent back-to-back publications [C. Gross et al., Nature (London) 464, 1165 (2010) and Max F. Riedel et al., Nature (London) 464, 1170 (2010)], reduced spin fluctuations are observed leading to spin squeezing at -8.2 and -2.5 dB, respectively, in two-component atomic condensates exhibiting one-axis-twisting interactions. The noise reduction limit for the one-axis twisting scales as ∝1/N(2/3), which for a condensate with N∼10(3) atoms is about 100 times below the standard quantum limit. We present a scheme using repeated Rabi pulses capable of transforming the one-axis-twisting spin squeezing into the two-axis-twisting type, leading to Heisenberg limited noise reduction ∝1/N or an extra tenfold improvement for N∼10(3).

Strongly enhanced spin squeezing via quantum control

We describe a new approach to spin squeezing based on a double-pass Faraday interaction between an optical probe and an optically dense atomic sample. A quantum eraser is used to remove residual spin-probe entanglement, thereby realizing a single-axis twisting unitary map on the collective spin. This interaction can be phase matched, resulting in exponential enhancement of squeezing as a function of optical density for times short compared to the decoherence time. In practice the scaling and peak squeezing depends on decoherence, technical loss, and noise. Including these imperfections, our model indicates that ∼10 dB of squeezing should be achievable with laboratory parameters.

Quantum nondemolition measurement of large-spin ensembles by dynamical decoupling

Quantum nondemolition (QND) measurement of collective variables by off-resonant optical probing has the ability to create entanglement and squeezing in atomic ensembles. Until now, this technique has been applied to real or effective spin one-half systems. We show theoretically that the buildup of Raman coherence prevents the naive application of this technique to larger spin atoms, but that dynamical decoupling can be used to recover the ideal QND behavior. We experimentally demonstrate dynamical decoupling by using a two-polarization probing technique. The decoupled QND measurement achieves a sensitivity 5.7(6) dB better than the spin projection noise.

Polarized alkali-metal vapor with minute-long transverse spin-relaxation time

We demonstrate lifetimes of Zeeman populations and coherences in excess of 60 sec in alkali-metal vapor cells with inner walls coated with an alkene material. This represents 2 orders of magnitude improvement over the best paraffin coatings. We explore the temperature dependence of cells coated with this material and investigate spin-exchange relaxation-free magnetometry in a room-temperature environment, a regime previously inaccessible with conventional coating materials.

Nonlinear atom interferometer surpasses classical precision limit

Interference is fundamental to wave dynamics and quantum mechanics. The quantum wave properties of particles are exploited in metrology using atom interferometers, allowing for high-precision inertia measurements. Furthermore, the state-of-the-art time standard is based on an interferometric technique known as Ramsey spectroscopy. However, the precision of an interferometer is limited by classical statistics owing to the finite number of atoms used to deduce the quantity of interest. Here we show experimentally that the classical precision limit can be surpassed using nonlinear atom interferometry with a Bose-Einstein condensate. Controlled interactions between the atoms lead to non-classical entangled states within the interferometer; this represents an alternative approach to the use of non-classical input states. Extending quantum interferometry to the regime of large atom number, we find that phase sensitivity is enhanced by 15 per cent relative to that in an ideal classical measurement. Our nonlinear atomic beam splitter follows the 'one-axis-twisting' scheme and implements interaction control using a narrow Feshbach resonance. We perform noise tomography of the quantum state within the interferometer and detect coherent spin squeezing with a squeezing factor of -8.2 dB (refs 11-15). The results provide information on the many-particle quantum state, and imply the entanglement of 170 atoms.

Implementation of cavity squeezing of a collective atomic spin

We squeeze unconditionally the collective spin of a dilute ensemble of laser-cooled 87Rb atoms using their interaction with a driven optical resonator. The shape and size of the resulting spin uncertainty region are well described by a simple analytical model [M. H. Schleier-Smith, I. D. Leroux, and V. Vuletić, arXiv:0911.3936 [Phys. Rev. A (to be published)]] through 2 orders of magnitude in the effective interaction strength, without free parameters. We deterministically generate states with up to 5.6(6) dB of metrologically relevant spin squeezing on the canonical 87Rb hyperfine clock transition.

States of an ensemble of two-level atoms with reduced quantum uncertainty

We generate entangled states of an ensemble of 5x10{4} 87Rb atoms by optical quantum nondemolition measurement. The resonator-enhanced measurement leaves the atomic ensemble, prepared in a superposition of hyperfine clock levels, in a squeezed spin state. By comparing the resulting reduction of quantum projection noise [up to 8.8(8) dB] with the concomitant reduction of coherence, we demonstrate a clock input state with spectroscopic sensitivity 3.0(8) dB beyond the standard quantum limit.

High bandwidth atomic magnetometery with continuous quantum nondemolition measurements

We describe an experimental study of spin-projection noise in a high sensitivity alkali-metal magnetometer. We demonstrate a fourfold improvement in the measurement bandwidth of the magnetometer using continuous quantum nondemolition measurements. Operating in the scalar mode with a measurement volume of 2 cm3 we achieve magnetic field sensitivity of 22 fT/Hz(1/2) and a bandwidth of 1.9 kHz with a spin polarization of only 1%. Our experimental arrangement is naturally backaction evading and can be used to realize sub-fT sensitivity with a highly polarized spin-squeezed atomic vapor.

Manipulation of nonclassical atomic spin states

We report successful manipulation of nonclassical atomic spin states. We apply an off-resonant noncircularly-polarized light pulse to a measurement-induced squeezed spin state of a cold atomic ensemble. By changing the pulse duration, we clearly observe a rotation of the anisotropic quantum-noise distribution in good contrast with the case of manipulation of a coherent spin state where the quantum-noise distribution is always isotropic. This is an important step for quantum state tomography, quantum swapping, and precision spectroscopic measurement.

Generation of two-mode squeezed and entangled light in a single temporal and spatial mode

We analyse a novel squeezing and entangling mechanism which is due to correlated Stokes and anti-Stokes photon forward scattering in a multi-level atom vapour. We develop a full quantum model for an alkali atomic vapour including quantized collective atomic states which predicts high degree of squeezing for attainable experimental conditions. Following the proposal we present an experimental demonstration of 3.5 dB pulsed frequency nondegenerate squeezed (quadrature entangled) state of light using room temperature caesium vapour. The source is very robust and requires only a few milliwatts of laser power. The squeezed state is generated in the same spatial mode as the local oscillator and in a single temporal mode. The two entangled modes are separated by twice the Zeeman frequency of the vapour which can be widely tuned. The narrow-band squeezed light generated near an atomic resonance can be directly used for atom-based quantum information protocols. Its single temporal mode characteristics make it a promising resource for quantum information processing.

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 greater, similar 10(5) 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.

Spin squeezing as an indicator of quantum chaos in the Dicke model

We study spin squeezing, an intrinsic quantum property, in the Dicke model without the rotating-wave approximation. We show that the spin squeezing can reveal the underlying chaotic and regular structures in phase space given by a Poincaré section, namely, it acts as an indicator of quantum chaos. Spin squeezing vanishes after a very short time for an initial coherent state centered in a chaotic region, whereas it persists over a longer time for the coherent state centered in a regular region of the phase space. We also study the distribution of the mean spin directions when quantum dynamics takes place. Finally, we discuss relations among spin squeezing, bosonic quadrature squeezing, and two-qubit entanglement in the dynamical processes.

Spin squeezing of a cold atomic ensemble with the nuclear spin of one-half

In order to establish an applicable system for advanced quantum information processing based on the interaction between light and atoms, we have demonstrated a quantum nondemolition measurement with a collective spin of cold ytterbium atoms (171Yb), and have observed 1.8(-1.5)+2.4 dB spin squeezing. Since 171Yb atoms have only a nuclear spin of one-half in the ground state, the system constitutes the simplest spin ensemble and is thus robust against decoherence. We used very short pulses with a width of 100 ns, and as a result the interaction time became much shorter than the decoherence time, which is important for multistep quantum information processing.

Establishing Einstein-Poldosky-Rosen channels between nanomechanics and atomic ensembles

We suggest interfacing nanomechanical systems via an optical quantum bus to atomic ensembles, for which means of high precision state preparation, manipulation, and measurement are available. This allows, in particular, for a quantum nondemolition Bell measurement, projecting the coupled system, atomic-ensemble-nanomechanical resonator, into an entangled EPR state. The entanglement is observable even for nanoresonators initially well above their ground states and can be utilized for teleportation of states from an atomic ensemble to the mechanical system.

Quantum nondemolition measurement of photon number via optical Kerr effect in an ultra-high-Q microtoroid cavity

We theoretically investigate a quantum nondemolition (QND) measurement with optical Kerr effect in an ultra-high-Q microtoroidal system. The analytical and numerical results predict that the present QND measurement scheme possesses a high sensitivity, which allows for detecting few photons or even single photons. Ultra-high-Q toroidal microcavity may provide a novel experimental platform to study quantum physics with nonlinear optics at low light levels.