Measuring measurement

Measurement connects the world of quantum phenomena to the world of classical events. It plays both a passive role, observing quantum systems, and an active one, preparing quantum states and controlling them. Surprisingly - in the light of the central status of measurement in quantum mechanics - there is no general recipe for designing a detector that measures a given observable. Compounding this, the characterization of existing detectors is typically based on partial calibrations or elaborate models. Thus, experimental specification (i.e. tomography) of a detector is of fundamental and practical importance. Here, we present the realization of quantum detector tomography: we identify the optimal positive-operator-valued measure describing the detector, with no ancillary assumptions. This result completes the triad, state, process, and detector tomography, required to fully specify an experiment. We characterize an avalanche photodiode and a photon number resolving detector capable of detecting up to eight photons. This creates a new set of tools for accurately detecting and preparing non-classical light.Comment: 6 pages, 4 figures,see video abstract at http://www.quantiki.org/video_abstracts/0807244

The Flat Transmission Spectrum of the Super-Earth GJ1214b from Wide Field Camera 3 on the Hubble Space Telescope

Capitalizing on the observational advantage offered by its tiny M dwarf host, we present HST/WFC3 grism measurements of the transmission spectrum of the super-Earth exoplanet GJ1214b. These are the first published WFC3 observations of a transiting exoplanet atmosphere. After correcting for a ramp-like instrumental systematic, we achieve nearly photon-limited precision in these observations, finding the transmission spectrum of GJ1214b to be flat between 1.1 and 1.7 microns. Inconsistent with a cloud-free solar composition atmosphere at 8.2 sigma, the measured achromatic transit depth most likely implies a large mean molecular weight for GJ1214b's outer envelope. A dense atmosphere rules out bulk compositions for GJ1214b that explain its large radius by the presence of a very low density gas layer surrounding the planet. High-altitude clouds can alternatively explain the flat transmission spectrum, but they would need to be optically thick up to 10 mbar or consist of particles with a range of sizes approaching 1 micron in diameter.Comment: 17 pages, 12 figures, accepted for publication in Ap

Generating Single Microwave Photons in a Circuit

Electromagnetic signals in circuits consist of discrete photons, though conventional voltage sources can only generate classical fields with a coherent superposition of many different photon numbers. While these classical signals can control and measure bits in a quantum computer (qubits), single photons can carry quantum information, enabling non-local quantum interactions, an important resource for scalable quantum computing. Here, we demonstrate an on-chip single photon source in a circuit quantum electrodynamics (QED) architecture, with a microwave transmission line cavity that collects the spontaneous emission of a single superconducting qubit with high efficiency. The photon source is triggered by a qubit rotation, as a photon is generated only when the qubit is excited. Tomography of both qubit and fluorescence photon shows that arbitrary qubit states can be mapped onto the photon state, demonstrating an ability to convert a stationary qubit into a flying qubit. Both the average power and voltage of the photon source are characterized to verify performance of the system. This single photon source is an important addition to a rapidly growing toolbox for quantum optics on a chip.Comment: 6 pages, 5 figures, hires version at http://www.eng.yale.edu/rslab/papers/single_photon_hires.pd

Qubit portrait of the photon-number tomogram and separability of two-mode light states

In view of the photon-number tomograms of two-mode light states, using the qubit-portrait method for studying the probability distributions with infinite outputs, the separability and entanglement detection of the states are studied. Examples of entangled Gaussian state and Schr\"{o}dinger cat state are discussed.Comment: 20 pages, 6 figures, TeX file, to appear in Journal of Russian Laser Researc

MuSR method and tomographic probability representation of spin states

Muon spin rotation/relaxation/resonance (MuSR) technique for studying matter structures is considered by means of a recently introduced probability representation of quantum spin states. A relation between experimental MuSR histograms and muon spin tomograms is established. Time evolution of muonium, anomalous muonium, and a muonium-like system is studied in the tomographic representation. Entanglement phenomenon of a bipartite muon-electron system is investigated via tomographic analogues of Bell number and positive partial transpose (PPT) criterion. Reconstruction of the muon-electron spin state as well as the total spin tomography of composed system is discussed.Comment: 20 pages, 4 figures, LaTeX, submitted to Journal of Russian Laser Researc

Efficient quantum state tomography

Quantum state tomography, the ability to deduce the state of a quantum system from measured data, is the gold standard for verification and benchmarking of quantum devices. It has been realized in systems with few components, but for larger systems it becomes infeasible because the number of quantum measurements and the amount of computation required to process them grows exponentially in the system size. Here we show that we can do exponentially better than direct state tomography for a wide range of quantum states, in particular those that are well approximated by a matrix product state ansatz. We present two schemes for tomography in 1-D quantum systems and touch on generalizations. One scheme requires unitary operations on a constant number of subsystems, while the other requires only local measurements together with more elaborate post-processing. Both schemes rely only on a linear number of experimental operations and classical postprocessing that is polynomial in the system size. A further strength of the methods is that the accuracy of the reconstructed states can be rigorously certified without any a priori assumptions.Comment: 9 pages, 4 figures. Combines many of the results in arXiv:1002.3780, arXiv:1002.3839, and arXiv:1002.4632 into one unified expositio

Subcycle Quantum Electrodynamics

Besides their stunning physical properties which are unmatched in a classical world, squeezed states of electromagnetic radiation bear advanced application potentials in quantum information systems and precision metrology, including gravitational wave detectors with unprecedented sensitivity. Since the first experiments on such nonclassical light, quantum analysis has been based on homodyning techniques and photon correlation measurements. These methods require a well-defined carrier frequency and photons contained in a quantum state need to be absorbed or amplified. They currently function in the visible to near-infrared and microwave spectral ranges. Quantum nondemolition experiments may be performed at the expense of excess fluctuations in another quadrature. Here we generate mid-infrared time-locked patterns of squeezed vacuum noise. After propagation through free space, the quantum fluctuations of the electric field are studied in the time domain by electro-optic sampling with few-femtosecond laser pulses. We directly compare the local noise amplitude to the level of bare vacuum fluctuations. This nonlinear approach operates off resonance without absorption or amplification of the field that is investigated. Subcycle intervals with noise level significantly below the pure quantum vacuum are found. Enhanced fluctuations in adjacent time segments manifest generation of highly correlated quantum radiation as a consequence of the uncertainty principle. Together with efforts in the far infrared, this work opens a window to the elementary quantum dynamics of light and matter in an energy range at the boundary between vacuum and thermal background conditions.Comment: 19 pages, 4 figure

Quantum tomography of an electron

International audienceThe complete knowledge of a quantum state allows the prediction of the probability of all possible measurement outcomes, a crucial step in quantum mechanics. It can be provided by tomographic methods which have been applied to atomic, molecular, spin and photonic states. For optical or microwave photons, standard tomogra-phy is obtained by mixing the unknown state with a large-amplitude coherent photon field. However, for fermions such as electrons in condensed matter, this approach is not applicable because fermionic fields are limited to small amplitudes (at most one particle per state), and so far no determination of an electron wavefunction has been made. Recent proposals involving quantum conductors suggest that the wavefunction can be obtained by measuring the time-dependent current of electronic wave interferometers or the current noise of electronic Hanbury-Brown/Twiss interferometers. Here we show that such measurements are possible despite the extreme noise sensitivity required, and present the reconstructed wavefunction quasi-probability, or Wigner distribution function, of single electrons injected into a ballistic conductor. Many identical electrons are prepared in well-controlled quantum states called levitons by repeatedly applying Lorentzian voltage pulses to a contact on the conductor. After passing through an electron beam splitter, the levitons are mixed with a weak-amplitude fermionic field formed by a coherent superposition of electron–hole pairs generated by a small alternating current with a frequency that is a multiple of the voltage pulse frequency 16. Antibunching of the electrons and holes with the levi-tons at the beam splitter changes the leviton partition statistics, and the noise variations provide the energy density matrix elements of the levitons. This demonstration of quantum tomography makes the developing field of electron quantum optics with ballistic conductors a new test-bed for quantum information with fermions. These results may find direct application in probing the entanglement of electron flying quantum bits, electron decoherence and electron interactions. They could also be applied to cold fermionic (or spin-1/2) atoms