Two-photon quantum interference at a beam splitter, commonly known as Hong-Ou-Mandel interference, was recently demonstrated with emph{microwave-frequency} photons by Lang emph{etal.}\,\cite{lang:microwaveHOM}. This experiment employed circuit QED systems as sources of microwave photons, and was based on the measurement of second-order cross-correlation and auto-correlation functions of the microwave fields at the outputs of the beam splitter. Here we present the calculation of these correlation functions for the cases of inputs corresponding to: (i) trains of \emph{pulsed} Gaussian or Lorentzian single microwave photons, and (ii) resonant fluorescent microwave fields from \emph{continuously-driven} circuit QED systems. The calculations include the effects of the finite bandwidth of the detection scheme. In both cases, the signature of two-photon quantum interference is a suppression of the second-order cross-correlation function for small delays. The experiment described in Ref. \onlinecite{lang:microwaveHOM} was performed with trains of \emph{Lorentzian} single photons, and very good agreement between the calculations and the experimental data was obtained.
Transferring the state of an information carrier from a sender to a receiver
is an essential primitive in both classical and quantum communication and
information processing. In a quantumprocess known as teleportation the unknown
state of a quantum bit can be relayed to a distant party using shared
entanglement and classical information. Here we present experiments in a
solid-state system based on superconducting quantum circuits demonstrating the
teleportation of the state of a qubit at the macroscopic scale. In our
experiments teleportation is realized deterministically with high efficiency
and achieves a high rate of transferred qubit states. This constitutes a
significant step towards the realization of repeaters for quantum communication
at microwave frequencies and broadens the tool set for quantum information
processing with superconducting circuits.
We make use of a superconducting qubit to study the effects of noise on
adiabatic geometric phases. The state of the system, an effective spin one-half
particle, is adiabatically guidedalong a closed path in parameter space and
thereby acquires a geometric phase. By introducing artificial fluctuations in
the control parameters, we measure the geometric contribution to dephasing for
a variety of noise powers and evolution times. Our results clearly show that
only fluctuations which distort the path lead to geometric dephasing. In a
direct comparison with the dynamic phase, which is path-independent, we observe
that the adiabatic geometric phase is less affected by noise-induced dephasing.
This observation directly points towards the potential of geometric phases for
quantum gates or metrological applications.
Interference at a beam splitter reveals both classical and quantum properties
of electromagnetic radiation. When two indistinguishable single photons impinge
at the two inputs of abeam splitter they coalesce into a pair of photons
appearing in either one of its two outputs. This effect is due to the bosonic
nature of photons and was first experimentally observed by Hong, Ou, and Mandel
(HOM) [1]. Here, we present the observation of the HOM effect with two
independent single-photon sources in the microwave frequency domain. We probe
the indistinguishability of single photons, created with a controllable delay,
in time-resolved second-order cross- and auto-correlation function
measurements. Using quadrature amplitude detection we are able to resolve
different photon numbers and detect coherence in and between the output arms.
This measurement scheme allows us to observe the HOM effect and, in addition,
to fully characterize the two-mode entanglement of the spatially separated beam
splitter output modes. Our experiments constitute a first step towards using
two-photon interference at microwave frequencies for quantum communication and
information processing, e.g. for distributing entanglement between nodes of a
quantum network [2, 3] and for linear optics quantum computation [4, 5].
Interference at a beam splitter reveals both classical and quantum properties of electromagnetic radiation. When two indistinguishable single photons impinge at the two inputs of abeam splitter they coalesce into a pair of photons appearing in either one of its two outputs. This effect is due to the bosonic nature of photons and was first experimentally observed by Hong, Ou, and Mandel (HOM) [1]. Here, we present the observation of the HOM effect with two independent single-photon sources in the microwave frequency domain. We probe the indistinguishability of single photons, created with a controllable delay, in time-resolved second-order cross- and auto-correlation function measurements. Using quadrature amplitude detection we are able to resolve different photon numbers and detect coherence in and between the output arms. This measurement scheme allows us to observe the HOM effect and, in addition, to fully characterize the two-mode entanglement of the spatially separated beam splitter output modes. Our experiments constitute a first step towards using two-photon interference at microwave frequencies for quantum communication and information processing, e.g. for distributing entanglement between nodes of a quantum network [2, 3] and for linear optics quantum computation [4, 5].
A localized qubit entangled with a propagating quantum field is well suited
to study non-local aspects of quantum mechanics and may also provide a channel
to communicate between spatiallyseparated nodes in a quantum network. Here, we
report the on demand generation and characterization of Bell-type entangled
states between a superconducting qubit and propagating microwave fields
composed of zero, one and two-photon Fock states. Using low noise linear
amplification and efficient data acquisition we extract all relevant
correlations between the qubit and the photon states and demonstrate
entanglement with high fidelity.
Recent progress in the development of superconducting circuits has enabled
the realization of interesting sources of nonclassical radiation at microwave
frequencies. Here, we discussfield quadrature detection schemes for the
experimental characterization of itinerant microwave photon fields and their
entanglement correlations with stationary qubits. In particular, we present
joint state tomography methods of a radiation field mode and a two-level
system. Including the case of finite quantum detection efficiency, we relate
measured photon field statistics to generalized quasi-probability distributions
and statistical moments for one-channel and two-channel detection. We also
present maximum-likelihood methods to reconstruct density matrices from
measured field quadrature histograms. Our theoretical investigations are
supported by the presentation of experimental data, for which microwave quantum
fields beyond the single-photon and Gaussian level have been prepared and
reconstructed.