In quantum mechanics, the concept of weak measurements allows for the description of a quantum system both in terms of the initial preparation and the final state (post-selection). This paradigm has ...been extensively studied theoretically and experimentally, but almost all of weak-measurement experiments carried out to date can be understood in terms of the classical (electromagnetic wave) theory of optics. Here, we present a quantum version in which the measurement apparatus deterministically entangles two distinct optical beams. We show that a single photon, when properly post-selected, can have an effect equal to that of eight photons: that is, in a system where a single photon has been calibrated to write a nonlinear phase shift of straight phio on a probe beam, we measure phase shifts as large as 8straight phio for appropriately post-selected single photons. This opens up a new regime for the study of entanglement of optical beams, as well as further investigations of the power of weak-value amplification for the measurement of small quantities.
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.
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 it
. It is now well understood that the group delay
-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 experiments
, and a recent work even claims that tunnelling may take no time at all
. There have also been efforts to identify a different timescale that would better describe how long a given particle spends in the barrier region
. Here we directly measure such a time by studying Bose-condensed
Rb 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 now
.
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.
Over the past years, much effort has gone towards generating interactions between two optical beams so strong that they could be observed at the level of individual photons1, 2, 3. Interactions this ...strong, beyond opening up a new regime in optics4, could lead to technologies such as all-optical quantum information processing5, 6. However, the extreme weakness of photon-photon scattering has hindered any attempt to observe such interactions at the level of single particles. Here we present an implementation of a strong optical nonlinearity using electromagnetically induced transparency7, and a direct measurement of the resulting nonlinear phase shift for single post-selected photons. We show that the observed phase shift depends not only on the incident intensity of the (coherent-state) input signal, but also in a discrete fashion on whether 0 or 1 photons are detected at the output. We believe that this constitutes the first direct measurement of the cross-phase shift due to single photons, whose presence or absence is established based on a discrete detection event. It opens a door to future studies of nonlinear optics in the quantum regime, and potential applications in areas such as quantum information processing.
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.
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.
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 87Rb 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.
As the separation between two emitters is decreased below the Rayleigh limit, the information that can be gained about their separation using traditional imaging techniques, photon counting in the ...image plane, reduces to nil. Assuming the sources are of equal intensity, Rayleigh's 'curse' can be alleviated by making phase-sensitive measurements in the image plane. However, with unequal and unknown intensities the curse returns regardless of the measurement, though the ideal scheme would still outperform image plane counting (IPC), i.e. recording intensities on a screen. We analyze the limits of the super-resolved position localization by inversion of coherence along an edge (SPLICE) phase measurement scheme as the intensity imbalance between the emitters grows. We find that SPLICE still outperforms IPC for moderately disparate intensities. For larger intensity imbalances we propose a hybrid of IPC and SPLICE, which we call 'adapted SPLICE', requiring only simple modifications. Using Monte Carlo simulation, we identify regions (emitter brightness, separation, intensity imbalance) where it is advantageous to use SPLICE over IPC, and when to switch to the adapted SPLICE measurement. We find that adapted SPLICE can outperform IPC for large intensity imbalances, e.g. 10 000:1, with the advantage growing with greater disparity between the two intensities. Finally, we also propose additional phase measurements for estimating the statistical moments of more complex source distributions. Our results are promising for implementing phase measurements in sub-Rayleigh imaging tasks such as exoplanet detection.
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