(a) Dissipative interaction prevents transmission of more than one photon at a time. Inset:
Normalized two-photon correlation function g( 2), displaying the antibunching of photons.
(b) Dispersive interaction alters the optical phase for two simultaneous photons (top). The
lower effective energy of two proximal photons leads to an attractive force, which bounds
photon pairs and gives rise to bunching (bottom).
|t1 – t2| (ms)
Two-photon probability g ( 2)
Detection time t1 (ms)
g ( 2)
0 0.5 1 1. 5
We controlled the interaction
properties by detuning the optical frequencies from the atomic resonances,
while keeping a high ( 50 percent)
overall transmission. For dissipative
interactions, a photon propagating in
the medium scattered and blocked the
subsequent photons with 95 percent
probability. For dispersive interactions,
we showed a phase shift of 1 radian for
two photons, very close to the ultimate
value of π required for quantum gates
and implying a Kerr effect 100 times
stronger than previously obtained.
Here, the quantum dynamics was
governed by a two-photon “molecule,”
or bound state, supported by the effective attraction between the photons.
Due to quantum dynamics, our system
produced entangled photon pairs from
initially independent photons. This
method could create quantum solitons,
correlated states of light and high-fidelity quantum gates.
Quantum-optics researchers have been trying to achieve strong interactions between individual photons for
decades. 1 These interactions constitute
a fundamental tool toward the ultimate
control of light fields “quantum by
quantum.” They can be used to realize
deterministic two-qubit optical gates
for scalable quantum computing and
to produce highly correlated states for
high-precision measurements. Also,
they enable the exploration of new
quantum states and phases, similar to
those explored in strongly correlated
particle systems. We have realized this
long-term goal and have observed both
dissipative and dispersive interactions
between individual photons. 2, 3
The interaction is mediated in a gas
of cold atoms by high-lying electronic
orbitals known as Rydberg atomic
states. Owing to their huge transition
dipole moments, the van der Walls
potential between Rydberg atoms,
growing as the orbital number (n) to
the power of 11, is substantial even
at distances of 10 µm for our chosen
state of n = 100. To ensure the ad hoc
excitation of a Rydberg atom per propagating photon, we utilize a slow-light
technique. 4, 5 A photon in our medium
is converted into a Rydberg polariton,
a mutual excitation of light and matter with an effective mass, where the
matter component is a Rydberg atom.
These Rydberg polaritons slow down
to 100 m/s (compared to c = 3 × 108 m/s
in vacuum), indicating 99.9999 percent
Rydberg excitation probability. Thus,
individual photons effectively acquire
large electric dipoles, long-range
interactions and mass.
and M.D. Lukin
MIT-Harvard Center for
Ultracold Atoms, Mass., U.S.A.
Q.-Y. Liang and V. Vuletic
NIST/University of Maryland, U. S.A.
University of Stuttgart, Germany
Max Planck Institute,
1. A. Imamoglu et al. Phys.
Rev. Lett. 79, 1467 (1997).
2. T. Peyronel et al. Nature
488, 57 (2012).
3. O. Firstenberg et al. Nature
502, 71 (2013).
4. M. Fleischhauer et al. Rev.
Mod. Phys. 77, 633 (2005).
5. J.D. Pritchard et al. Ann. Rev.
Cold At. Mol. 1, 301 (2013).
Quantum Nonlinear Optics:
Strongly Interacting Photons