Spin Rotations in a Bose-Einstein Condensate Driven by Counterflow and Spin-Independent Interactions.

We observe spin rotations caused by atomic collisions in a nonequilibrium Bose-condensed gas of ^{87}Rb. Reflection from a pseudomagnetic barrier creates counterflow in which forward- and backward-propagating matter waves have partly transverse spin directions. Even though inter-atomic interaction strengths are state independent, the indistinguishability of parallel spins leads to spin dynamics. A local magnetodynamic model, which captures the salient features of the observed spin textures, highlights an essential connection between four-wave mixing and collisional spin rotation. The observed phenomenon is commonly thought not to occur in Bose condensates; our observations and model clarify the nature of these effective-magnetic spin rotations.

Negative Quasiprobabilities Enhance Phase Estimation in Quantum-Optics Experiment.

Operator noncommutation, a hallmark of quantum theory, limits measurement precision, according to uncertainty principles. Wielded correctly, though, noncommutation can boost precision. A recent foundational result relates a metrological advantage with negative quasiprobabilities-quantum extensions of probabilities-engendered by noncommuting operators. We crystallize the relationship in an equation that we prove theoretically and observe experimentally. Our proof-of-principle optical experiment features a filtering technique that we term partially postselected amplification (PPA). Using PPA, we measure a wave plate's birefringent phase. PPA amplifies, by over two orders of magnitude, the information obtained about the phase per detected photon. In principle, PPA can boost the information obtained from the average filtered photon by an arbitrarily large factor. The filter's amplification of systematic errors, we find, bounds the theoretically unlimited advantage in practice. PPA can facilitate any phase measurement and mitigates challenges that scale with trial number, such as proportional noise and detector saturation. By quantifying PPA's metrological advantage with quasiprobabilities, we reveal deep connections between quantum foundations and precision measurement.

Observation of the Decrease of Larmor Tunneling Times with Lower Incident Energy.

How much time does a tunneling particle spend in a barrier? A Larmor clock, one proposal to answer this question, measures the interaction between the particle and the barrier region using an auxiliary degree of freedom of the particle to clock the dwell time inside the barrier. We report on precise Larmor time measurements of ultracold ^{87}Rb atoms tunneling through an optical barrier, which confirm longstanding predictions of tunneling times. We observe that atoms generally spend less time tunneling through higher barriers and that this time decreases for lower energy particles. For the lowest measured incident energy, at least 90% of transmitted atoms tunneled through the barrier, spending an average of 0.59±0.02 ms inside. This is 0.11±0.03 ms faster than atoms traversing the same barrier with energy close to the barrier's peak and 0.21±0.03 ms faster than when the atoms traverse a barrier with 23% less energy.

Measurement of the time spent by a tunnelling atom within the barrier region.

Tunnelling is one of the most characteristic phenomena of quantum physics, underlying processes such as photosynthesis and nuclear fusion, as well as devices ranging from superconducting quantum interference device (SQUID) magnetometers to superconducting qubits for quantum computers. The question of how long a particle takes to tunnel through a barrier, however, has remained contentious since the first attempts to calculate it1. It is now well understood that the group delay2-the arrival time of the peak of the transmitted wavepacket at the far side of the barrier-can be smaller than the barrier thickness divided by the speed of light, without violating causality. This has been confirmed by many experiments3-6, and a recent work even claims that tunnelling may take no time at all7. There have also been efforts to identify a different timescale that would better describe how long a given particle spends in the barrier region8-10. Here we directly measure such a time by studying Bose-condensed 87Rb atoms tunnelling through a 1.3-micrometre-thick optical barrier. By localizing a pseudo-magnetic field inside the barrier, we use the spin precession of the atoms as a clock to measure the time that they require to cross the classically forbidden region. We study the dependence of the traversal time on the incident energy, finding a value of 0.61(7) milliseconds at the lowest energy for which tunnelling is observable. This experiment lays the groundwork for addressing fundamental questions about history in quantum mechanics: for instance, what we can learn about where a particle was at earlier times by observing where it is now11-13.

Beating Rayleigh's Curse by Imaging Using Phase Information.

Every imaging system has a resolution limit, typically defined by Rayleigh's criterion. Given a fixed number of photons, the amount of information one can gain from an image about the separation between two sources falls to zero as the separation drops below this limit, an effect dubbed "Rayleigh's curse." Recently, in a quantum-information-inspired proposal, Tsang and co-workers found that there is, in principle, infinitely more information present in the full electromagnetic field in the image plane than in the intensity alone, and suggested methods for extracting this information and beating the Rayleigh limit. In this Letter, we experimentally demonstrate a simple scheme that captures most of this information, and show that it has a greatly improved ability to estimate the distance between a pair of closely separated sources, achieving near-quantum-limited performance and immunity to Rayleigh's curse.

Interaction-Assisted Quantum Tunneling of a Bose-Einstein Condensate Out of a Single Trapping Well.

We experimentally study tunneling of Bose-condensed ^{87}Rb atoms prepared in a quasibound state and observe a nonexponential decay caused by interatomic interactions. A combination of a magnetic quadrupole trap and a thin 1.3 µm barrier created using a blue-detuned sheet of light is used to tailor traps with controllable depth and tunneling rate. The escape dynamics strongly depend on the mean-field energy, which gives rise to three distinct regimes-classical spilling over the barrier, quantum tunneling, and decay dominated by background losses. We show that the tunneling rate depends exponentially on the chemical potential. Our results show good agreement with numerical solutions of the 3D Gross-Pitaevskii equation.

Experimental Demonstration of the Effectiveness of Electromagnetically Induced Transparency for Enhancing Cross-Phase Modulation in the Short-Pulse Regime.

We present an experiment using a sample of laser-cooled Rb atoms to show that cross-phase modulation schemes continue to benefit from electromagnetically induced transparency (EIT) even as the transparency window is made narrower than the signal bandwidth (i.e., for signal pulses much shorter than the response time of the EIT system). Addressing concerns that narrow EIT windows might not prove useful for such applications, we show that while the peak phase shift saturates in this regime, it does not drop, and the time-integrated effect continues to scale inversely with EIT window width. This integrated phase shift is an important figure of merit for tasks such as the detection of single-photon-induced cross-phase shifts. Only when the window width approaches the system's dephasing rate γ does the peak phase shift begin to decrease, leading to an integrated phase shift that peaks when the window width is equal to 4γ.

Quantum data compression of a qubit ensemble.

Data compression is a ubiquitous aspect of modern information technology, and the advent of quantum information raises the question of what types of compression are feasible for quantum data, where it is especially relevant given the extreme difficulty involved in creating reliable quantum memories. We present a protocol in which an ensemble of quantum bits (qubits) can in principle be perfectly compressed into exponentially fewer qubits. We then experimentally implement our algorithm, compressing three photonic qubits into two. This protocol sheds light on the subtle differences between quantum and classical information. Furthermore, since data compression stores all of the available information about the quantum state in fewer physical qubits, it could allow for a vast reduction in the amount of quantum memory required to store a quantum ensemble, making even today's limited quantum memories far more powerful than previously recognized.

Experimental demonstration of a flexible time-domain quantum channel.

We present an experimental realization of a flexible quantum channel where the Hilbert space dimensionality can be controlled electronically. Using electro-optical modulators (EOM) and narrow-band optical filters, quantum information is encoded and decoded in the temporal degrees of freedom of photons from a long-coherence-time single-photon source. Our results demonstrate the feasibility of a generic scheme for encoding and transmitting multidimensional quantum information over the existing fiber-optical telecommunications infrastructure.

Scalable spatial superresolution using entangled photons.

N00N states-maximally path-entangled states of N photons-exhibit spatial interference patterns sharper than any classical interference pattern. This is known as superresolution. However, even given perfectly efficient number-resolving detectors, the detection efficiency of all previous measurements of such interference would decrease exponentially with the number of photons in the N00N state, often leading to the conclusion that N00N states are unsuitable for spatial measurements. A technique known as the "optical centroid measurement" has been proposed to solve this and has been experimentally verified for photon pairs; here we present the first extension beyond two photons, measuring the superresolution fringes of two-, three-, and four-photon N00N states. Moreover, we compare the N00N-state interference to the corresponding classical superresolution interference. Although both provide the same increase in spatial frequency, the visibility of the classical fringes decreases exponentially with the number of detected photons. Our work represents an essential step forward for quantum-enhanced measurements, overcoming what was believed to be a fundamental challenge to quantum metrology.

Observing the onset of effective mass.

The response of a particle in a periodic potential to an applied force is commonly described by an effective mass, which accounts for the detailed interaction between the particle and the surrounding potential. Using a Bose-Einstein condensate of (87)Rb atoms initially in the ground band of an optical lattice, we experimentally show that the initial response of a particle to an applied force is in fact characterized by the bare mass. Subsequently, the particle response undergoes rapid oscillations and only over time scales that are long compared to those of the interband dynamics is the effective mass observed to be an appropriate description. Our results elucidate the role of the effective mass on short time scales, which is relevant for example in the interaction of few-cycle laser pulses with dielectric and semiconductor materials.

Enhanced coherence between condensates formed resonantly at different times.

We demonstrate coherence between exciton-polariton condensates created resonantly at different times. The coherence persists much longer than the individual particle dephasing time, and this persistence increases as the particle density increases. The observed coherence time exceeds that of the injecting laser pulse by more than an order of magnitude. We show that this significant coherence enhancement relies critically on the many-body particle interactions, as verified by its dependence on particle density, interaction strength, and bath temperature, whereas the mass of the particles plays no role in the condensation of resonantly injected polaritons. Furthermore, we observe a large nonlinear phase shift resulting from intra-condensate interaction energy. Our results provide a new approach for probing ultrafast dynamics of resonantly-created condensates and open new directions in the study of coherence in matter.

Coherent control of population transfer between vibrational states in an optical lattice via two-path quantum interference.

We demonstrate coherent control of population transfer between vibrational states in an optical lattice by using interference between a one-phonon transition at 2ω and a two-phonon transition at ω. The ω and 2ω transitions are driven by phase- and amplitude-modulation of the lattice laser beams, respectively. By varying the relative phase of these two pathways, we control the branching ratio between transitions to the first excited state and those to the higher states. Our best result shows a branching ratio of 17±2, which is the highest among coherent control experiments using analogous schemes. Such quantum control techniques may find broad application in suppressing leakage errors in a variety of quantum information architectures.

Violation of Heisenberg's measurement-disturbance relationship by weak measurements.

While there is a rigorously proven relationship about uncertainties intrinsic to any quantum system, often referred to as "Heisenberg's uncertainty principle," Heisenberg originally formulated his ideas in terms of a relationship between the precision of a measurement and the disturbance it must create. Although this latter relationship is not rigorously proven, it is commonly believed (and taught) as an aspect of the broader uncertainty principle. Here, we experimentally observe a violation of Heisenberg's "measurement-disturbance relationship", using weak measurements to characterize a quantum system before and after it interacts with a measurement apparatus. Our experiment implements a 2010 proposal of Lund and Wiseman to confirm a revised measurement-disturbance relationship derived by Ozawa in 2003. Its results have broad implications for the foundations of quantum mechanics and for practical issues in quantum measurement.

Dynamic Stark effect in strongly coupled microcavity exciton polaritons.

We present experimental observations of a nonresonant dynamic Stark shift in strongly coupled microcavity quantum well exciton polaritons--a system which provides a rich variety of solid-state collective phenomena. The Stark effect is demonstrated in a GaAs/AlGaAs system at 10 K by femtosecond pump-probe measurements, with the blueshift approaching the meV scale for a pump fluence of 2 mJ cm(-2) and 50 meV red detuning, in good agreement with theory. The energy level structure of the strongly coupled polariton Rabi doublet remains unaffected by the blueshift. The demonstrated effect should allow generation of ultrafast density-independent potentials and imprinting well-defined phase profiles on polariton condensates, providing a powerful tool for manipulation of these condensates, similar to dipole potentials in cold-atom systems.

Multidimensional quantum information based on single-photon temporal wavepackets.

We propose a multidimensional quantum information encoding approach based on temporal modulation of single photons, where the Hilbert space can be spanned by an in-principle infinite set of orthonormal temporal profiles. We analyze two specific realizations of such modulation schemes, and show that error rate per symbol can be smaller than 1% for practical implementations. Temporal modulation may enable multidimensional quantum communication over the existing fiber optical infrastructure, as well as provide an avenue for probing high-dimensional entanglement approaching the continuous limit.

Amplifying single-photon nonlinearity using weak measurements.

We show that weak measurement can be used to "amplify" optical nonlinearities at the single-photon level, such that the effect of one properly postselected photon on a classical beam may be as large as that of many unpostselected photons. We find that "weak-value amplification" offers a marked improvement in the signal-to-noise ratio in the presence of technical noise with long correlation times. Unlike previous weak-measurement experiments, our proposed scheme has no classical equivalent.

Observing the average trajectories of single photons in a two-slit interferometer.

A consequence of the quantum mechanical uncertainty principle is that one may not discuss the path or "trajectory" that a quantum particle takes, because any measurement of position irrevocably disturbs the momentum, and vice versa. Using weak measurements, however, it is possible to operationally define a set of trajectories for an ensemble of quantum particles. We sent single photons emitted by a quantum dot through a double-slit interferometer and reconstructed these trajectories by performing a weak measurement of the photon momentum, postselected according to the result of a strong measurement of photon position in a series of planes. The results provide an observationally grounded description of the propagation of subensembles of quantum particles in a two-slit interferometer.

Closed timelike curves via postselection: theory and experimental test of consistency.

Closed timelike curves (CTCs) are trajectories in spacetime that effectively travel backwards in time: a test particle following a CTC can interact with its former self in the past. A widely accepted quantum theory of CTCs was proposed by Deutsch. Here we analyze an alternative quantum formulation of CTCs based on teleportation and postselection, and show that it is inequivalent to Deutsch's. The predictions or retrodictions of our theory can be simulated experimentally: we report the results of an experiment illustrating how in our particular theory the "grandfather paradox" is resolved.