*C. Ell, H. M. Gibbs, G. Khitrova,
E. S. Lee, and S. Park
Optical Sciences Center,
University of Arizona,
Tucson, AZ 85721*

*and*

*D. G. Deppe and D. L. Huffaker,
Microelectronics Research Center,
University of Texas,
Austin, TX 78712-1100 *

A quantum dot in a semiconductor nanocavity, exhibiting single-exciton/ single-photon strong coupling, is proposed as a solid-state system for quantum entanglement. The key is lateral confinement to minimize the cavity- mode volume.

A quantum well grown in the center of a semiconductor microcavity gives rise to a nonperturbative light-matter interaction resulting in two transmission peaks and reflection dips – the normal-mode-coupling between one cavity mode and one exciton resonance [1]. This effect is often related to vacuum-field Rabi (VRS) splitting of atoms or to a polariton describing light propagation in a medium. The regime of many-oscillator vacuum-field Rabi splitting was reached in the early 1980’s using many atoms in a cavity - after years of hard work to improve the cavity quality factor Q, to make the photon escape rate less than the many-atom VRS oscillation rate. After a decade of gradual improvements, vacuum-field Rabi splitting was seen with a single atom [2,3]; this led to the first clear demonstration of the discrete nature of the coherent exchange of energy between the atom and the quantized electromagnetic field [4]. For such a truly quantum system the optical properties are changed by the addition of a single photon or a single atom.

Present-day semiconductor microcavities showing normal-mode coupling, however, are
still in the opposite limit, the limit of many atoms, where many photons are needed to
change the optical properties. This system behaves semiclassically, i.e., the light-matter
interaction can be described equally well on the basis of a classical field in linear and
nonlinear studies [5-8]. E.g., we measured 2 ´ 10^{5}
photons to be absorbed nonresonantly from a 150-*fs* pulse in a 50-*µm*-diameter
beam to reduce the peak exciton absorption coefficient by two and the VRS transmission by
five [9]. Thus we are far from the quantum limit. It is the very large QW absorption
coefficient, i.e., the potential for the formation of many excitons, that gives rise to
the VRS, much like the many-atom case. To obtain a useful quantum gate, the number of
oscillators causing the VRS must be reduced to one [10]. Then the oscillator-cavity system
will be truly quantum; a second photon will feel the first-photon/ exciton entanglement.
And expectation values of matter-field operators cannot be factored into a product of a
matter expectation value and a field expectation value.

The following questions are addressed here. How can we realize a quantum
dot that would reduce the potential of forming many excitons? Can the vacuum field be
increased sufficiently by reducing the cavity-mode volume, so that a single quantum dot
can exhibit VRS similar to an atom in a high-finesse cavity [11,12]? Such a quantum-dot
nanocavity has two advantages: a length close to the theoretical minimum and a much larger
dipole moment permitting a strong coupling without an ultra high-Q cavity even for such a
short length. The single-atom VRS is *g*_{0} = *µE _{vac}*.
The vacuum field

Thus

the larger the dipole moment µ of the oscillator and the smaller the cavity-mode waist
w0 and length Lcav, the larger the splitting 2*g _{0}*.

While the cavity length for a 1l spacer is already close to
its minimum value of *L _{cav}* » 1

To see vacuum-Rabi splitting, *g _{0}* must exceed the photon decay rate d

where *µ*^{2}/*A _{QW}* is a constant. For a QW with

Since this value exceeds VRS linewidths already achieved in present-day quantum-well
microcavities [8], such a small-diameter QW, that can be considered as a big “quantum
dot”, should reach the quantum limit. Finally, we show that the regime of true strong
coupling is also conceivable using the well-studied monolayer-fluctuation quantum dot of
Gammon et al. [19] in a nanocavity with cavity-mode volume of (1*µm*)^{3}.
Already Gutbrod et al. [20] report a 2-*meV* VRS splitting for a QW in a 1.2- *µm*
-diameter “photon dot.” And an aluminum-native-oxide aperture around quantum
dots has led to a record-low-threshold VCSEL [14]. In a monolayer-fluctuation dot,
fluctuations by one monolayer in the height of the GaAs surface result in several-meV
potential wells for lateral confinement. Nonlinear optical experiments [21] on such a 40-*nm*
dot conclude that it behaves like an atom; this would seem to imply that dephasing is
dominated by radiative decay. However, Fan et al. [22] studied the same dots and concluded
that the radiative recombination time » 4´
the dephasing time. Since the radiative rate in a dielectric medium is

where

is the free-space radiative rate [23,24],

The cavity photon decay rate is given by

.

Compare parameters of a quantum-dot [19] nanocavity, with mirror reflectivity of 99.8%,
with those in parentheses for a cold Cs atom [12,25]: l_{0}
= 830*nm* (852.4*nm*); t = 4 × 29*ps* (32*ns*);
e_{0} = 13 (1); *w*_{0} = 1*µm*
(13.5*µm*); *L _{cav}* = 1

Support is acknowledged in Tucson from AFOSR/DARPA, JSOP (AFOSR, ARO) and NSF (AMOP, EPDT) and in Austin from the University of New Mexico DARPA sponsored Optoelectronic Materials Center.

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Toward Quantum Entanglement In A Quantum-Dot Nanocavity

Epitaxial long wavelength DBRs on InP: AlAsSb or lateral oxidation

High Temperature 1300 nm VCSELs for single-mode fiber-optic communication

Manufacturing of Oxide VCSEL at Hewlett Packard