121 research outputs found
Is there a no-go theorem for superradiant quantum phase transitions in cavity and circuit QED ?
In cavity quantum electrodynamics (QED), the interaction between an atomic
transition and the cavity field is measured by the vacuum Rabi frequency
. The analogous term "circuit QED" has been introduced for Josephson
junctions, because superconducting circuits behave as artificial atoms coupled
to the bosonic field of a resonator. In the regime with comparable
to the two-level transition frequency, "superradiant" quantum phase transitions
for the cavity vacuum have been predicted, e.g. within the Dicke model. Here,
we prove that if the time-independent light-matter Hamiltonian is considered, a
superradiant quantum critical point is forbidden for electric dipole atomic
transitions due to the oscillator strength sum rule. In circuit QED, the
capacitive coupling is analogous to the electric dipole one: yet, such no-go
property can be circumvented by Cooper pair boxes capacitively coupled to a
resonator, due to their peculiar Hilbert space topology and a violation of the
corresponding sum rule
Quantum jumps of light recording the birth and death of a photon in a cavity
A microscopic system under continuous observation exhibits at random times
sudden jumps between its states. The detection of this essential quantum
feature requires a quantum non-demolition (QND) measurement repeated many times
during the system evolution. Quantum jumps of trapped massive particles
(electrons, ions or molecules) have been observed, which is not the case of the
jumps of light quanta. Usual photodetectors absorb light and are thus unable to
detect the same photon twice. They must be replaced by a transparent counter
'seeing' photons without destroying them3. Moreover, the light has to be stored
over a duration much longer than the QND detection time. We have fulfilled
these challenging conditions and observed photon number quantum jumps.
Microwave photons are stored in a superconducting cavity for times in the
second range. They are repeatedly probed by a stream of non-absorbing atoms. An
atom interferometer measures the atomic dipole phase shift induced by the
non-resonant cavity field, so that the final atom state reveals directly the
presence of a single photon in the cavity. Sequences of hundreds of atoms
highly correlated in the same state, are interrupted by sudden
state-switchings. These telegraphic signals record, for the first time, the
birth, life and death of individual photons. Applying a similar QND procedure
to mesoscopic fields with tens of photons opens new perspectives for the
exploration of the quantum to classical boundary
Nonlinear response of the vacuum Rabi resonance
On the level of single atoms and photons, the coupling between atoms and the
electromagnetic field is typically very weak. By employing a cavity to confine
the field, the strength of this interaction can be increased many orders of
magnitude to a point where it dominates over any dissipative process. This
strong-coupling regime of cavity quantum electrodynamics has been reached for
real atoms in optical cavities, and for artificial atoms in circuit QED and
quantum-dot systems. A signature of strong coupling is the splitting of the
cavity transmission peak into a pair of resolvable peaks when a single resonant
atom is placed inside the cavity - an effect known as vacuum Rabi splitting.
The circuit QED architecture is ideally suited for going beyond this linear
response effect. Here, we show that increasing the drive power results in two
unique nonlinear features in the transmitted heterodyne signal: the
supersplitting of each vacuum Rabi peak into a doublet, and the appearance of
additional peaks with the characteristic sqrt(n) spacing of the Jaynes-Cummings
ladder. These constitute direct evidence for the coupling between the quantized
microwave field and the anharmonic spectrum of a superconducting qubit acting
as an artificial atom.Comment: 6 pages, 4 figures. Supplementary Material and Supplementary Movies
are available at http://www.eng.yale.edu/rslab/publications.htm
Cavity QED with a Bose-Einstein condensate
Cavity quantum electrodynamics (cavity QED) describes the coherent
interaction between matter and an electromagnetic field confined within a
resonator structure, and is providing a useful platform for developing concepts
in quantum information processing. By using high-quality resonators, a strong
coupling regime can be reached experimentally in which atoms coherently
exchange a photon with a single light-field mode many times before dissipation
sets in. This has led to fundamental studies with both microwave and optical
resonators. To meet the challenges posed by quantum state engineering and
quantum information processing, recent experiments have focused on laser
cooling and trapping of atoms inside an optical cavity. However, the tremendous
degree of control over atomic gases achieved with Bose-Einstein condensation
has so far not been used for cavity QED. Here we achieve the strong coupling of
a Bose-Einstein condensate to the quantized field of an ultrahigh-finesse
optical cavity and present a measurement of its eigenenergy spectrum. This is a
conceptually new regime of cavity QED, in which all atoms occupy a single mode
of a matter-wave field and couple identically to the light field, sharing a
single excitation. This opens possibilities ranging from quantum communication
to a wealth of new phenomena that can be expected in the many-body physics of
quantum gases with cavity-mediated interactions.Comment: 6 pages, 4 figures; version accepted for publication in Nature;
updated Fig. 4; changed atom numbers due to new calibratio
Climbing the Jaynes-Cummings Ladder and Observing its Sqrt(n) Nonlinearity in a Cavity QED System
The already very active field of cavity quantum electrodynamics (QED),
traditionally studied in atomic systems, has recently gained additional
momentum by the advent of experiments with semiconducting and superconducting
systems. In these solid state implementations, novel quantum optics experiments
are enabled by the possibility to engineer many of the characteristic
parameters at will. In cavity QED, the observation of the vacuum Rabi mode
splitting is a hallmark experiment aimed at probing the nature of matter-light
interaction on the level of a single quantum. However, this effect can, at
least in principle, be explained classically as the normal mode splitting of
two coupled linear oscillators. It has been suggested that an observation of
the scaling of the resonant atom-photon coupling strength in the
Jaynes-Cummings energy ladder with the square root of photon number n is
sufficient to prove that the system is quantum mechanical in nature. Here we
report a direct spectroscopic observation of this characteristic quantum
nonlinearity. Measuring the photonic degree of freedom of the coupled system,
our measurements provide unambiguous, long sought for spectroscopic evidence
for the quantum nature of the resonant atom-field interaction in cavity QED. We
explore atom-photon superposition states involving up to two photons, using a
spectroscopic pump and probe technique. The experiments have been performed in
a circuit QED setup, in which ultra strong coupling is realized by the large
dipole coupling strength and the long coherence time of a superconducting qubit
embedded in a high quality on-chip microwave cavity.Comment: ArXiv version of manuscript published in Nature in July 2008, 5
pages, 5 figures, hi-res version at
http://www.finkjohannes.com/SqrtNArxivPreprint.pd
Ultrafast nonlocal control of spontaneous emission
Solid-state cavity quantum electrodynamics systems will form scalable nodes
of future quantum networks, allowing the storage, processing and retrieval of
quantum bits, where a real-time control of the radiative interaction in the
cavity is required to achieve high efficiency. We demonstrate here the dynamic
molding of the vacuum field in a coupled-cavity system to achieve the ultrafast
nonlocal modulation of spontaneous emission of quantum dots in photonic crystal
cavities, on a timescale of ~200 ps, much faster than their natural radiative
lifetimes. This opens the way to the ultrafast control of semiconductor-based
cavity quantum electrodynamics systems for application in quantum interfaces
and to a new class of ultrafast lasers based on nano-photonic cavities.Comment: 15 pages, 4 figure
Circuit Quantum Electrodynamics: Coherent Coupling of a Single Photon to a Cooper Pair Box
Under appropriate conditions, superconducting electronic circuits behave
quantum mechanically, with properties that can be designed and controlled at
will. We have realized an experiment in which a superconducting two-level
system, playing the role of an artificial atom, is strongly coupled to a single
photon stored in an on-chip cavity. We show that the atom-photon coupling in
this circuit can be made strong enough for coherent effects to dominate over
dissipation, even in a solid state environment. This new regime of matter light
interaction in a circuit can be exploited for quantum information processing
and quantum communication. It may also lead to new approaches for single photon
generation and detection.Comment: 8 pages, 4 figures, accepted for publication in Nature, embargo does
apply, version with high resolution figures available at:
http://www.eng.yale.edu/rslab/Andreas/content/science/PubsPapers.htm
Scheme for generating entangled states of two field modes in a cavity
This paper considers a two-level atom interacting with two cavity modes with
equal frequencies. Applying a unitary transformation, the system reduces to the
analytically solvable Jaynes-Cummings model. For some particular field states,
coherent and squeezed states, the transformation between the two bare basis's,
related by the unitary transformation, becomes particularly simple. It is shown
how to generate, the highly non-classical, entangled coherent states of the two
modes, both in the zero and large detuning cases. An advantage with the zero
detuning case is that the preparation is deterministic and no atomic
measurement is needed. For the large detuning situation a measurement is
required, leaving the field in either of two orthogonal entangled coherent
states.Comment: Accepted in J. Mod. Opt.; 12 pages; Replaced with revised version.
Extended discussion of experimental realizations, earlier studies in the
field and on the frequency dependence in the adiabatic eliminatio
Resolving photon number states in a superconducting circuit
Electromagnetic signals are always composed of photons, though in the circuit
domain those signals are carried as voltages and currents on wires, and the
discreteness of the photon's energy is usually not evident. However, by
coupling a superconducting qubit to signals on a microwave transmission line,
it is possible to construct an integrated circuit where the presence or absence
of even a single photon can have a dramatic effect. This system is called
circuit quantum electrodynamics (QED) because it is the circuit equivalent of
the atom-photon interaction in cavity QED. Previously, circuit QED devices were
shown to reach the resonant strong coupling regime, where a single qubit can
absorb and re-emit a single photon many times. Here, we report a circuit QED
experiment which achieves the strong dispersive limit, a new regime of cavity
QED in which a single photon has a large effect on the qubit or atom without
ever being absorbed. The hallmark of this strong dispersive regime is that the
qubit transition can be resolved into a separate spectral line for each photon
number state of the microwave field. The strength of each line is a measure of
the probability to find the corresponding photon number in the cavity. This
effect has been used to distinguish between coherent and thermal fields and
could be used to create a photon statistics analyzer. Since no photons are
absorbed by this process, one should be able to generate non-classical states
of light by measurement and perform qubit-photon conditional logic, the basis
of a logic bus for a quantum computer.Comment: 6 pages, 4 figures, hi-res version at
http://www.eng.yale.edu/rslab/papers/numbersplitting_hires.pd
Determining the Quantum Expectation Value by Measuring a Single Photon
Quantum mechanics, one of the keystones of modern physics, exhibits several
peculiar properties, differentiating it from classical mechanics. One of the
most intriguing is that variables might not have definite values. A complete
quantum description provides only probabilities for obtaining various
eigenvalues of a quantum variable. These and corresponding probabilities
specify the expectation value of a physical observable, which is known to be a
statistical property of an ensemble of quantum systems. In contrast to this
paradigm, we demonstrate a unique method allowing to measure the expectation
value of a physical variable on a single particle, namely, the polarisation of
a single protected photon. This is the first realisation of quantum protective
measurements.Comment: Nature Physics, in press (this version corresponds to the one
initially submitted to Nature Physics
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