Phase control of electron population, absorption, and dispersion properties of a semiconductor
quantum well
J. F. Dynes*
London Center for Nanotechnology, London WC1H 0AH, United Kingdom
E. Paspalakis
†
Materials Science Department, School of Natural Sciences, University of Patras, Patras 265 04, Greece
Received 16 January 2006; revised manuscript received 25 April 2006; published 16 June 2006
We show that an asymmetric semiconductor quantum well that forms a three-level cascade configuration can
be controlled by the relative phase of a laser field and its second harmonic. The electron population in the three
subbands and the probe absorption/dispersion spectra are crucially phase dependent. As an example, electron
inversion between the upper and lower subbands and change of the spectrum from absorption to gain is found
by solely varying the relative phase of the two fields.
DOI: 10.1103/PhysRevB.73.233305 PACS numbers: 78.67.De, 32.80.-t, 42.50.Gy, 42.50.Hz
In the past decade several quantum optical coherence and
interference effects
1,2
have been studied theoretically and ex-
perimentally in intersubband transitions ISBTs in the con-
duction band of semiconductor quantum wells QWs. Some
of these phenomena are tunneling induced transparency,
3,4
electromagnetically induced transparency,
5–7
pulsed-induced
quantum interference,
8
Autler-Townes splitting,
9
gain with-
out inversion,
10–13
enhanced second harmonic
generation,
14,15
enhanced index of refraction without
absorption,
16
coherently induced one-dimensional photonic
band gaps,
17
and coherent population trapping.
18
In addition,
extremely useful devices such as ultrafast optical
switches,
19–21
quantum switches,
22
and sensitive infrared
detectors
23
are based on quantum optical coherence and in-
terference effects in ISBTs in QWs.
Furthermore, the relative phase of applied laser fields has
been widely used for the coherent control of several impor-
tant processes in atomic, molecular, and solid-state
systems.
24
This method is usually termed as phase control.
Phase control has already been applied for the coherent ma-
nipulation of coherent population trapping,
25
coherent popu-
lation transfer,
26
and electromagnetically induced
transparency
27,28
in a closed-loop four-level atomic system.
Also, the simultaneous excitation of a two-level atom by a
fundamental laser field and its third harmonic can also lead
to the phase control of light propagation in this medium.
29
In
the area of semiconductors intensive interest has been given
to the control of photocurrent directionality by simultaneous
excitation of the semiconductors by a fundamental laser field
and its second harmonic.
30–34
In the present brief report, we study phase control of an
asymmetric semiconductor quantum well by simultaneous
application of a laser field and its second harmonic. We con-
sider an asymmetric quantum well structure with three en-
ergy levels that forms the well-known “cascade” configura-
tion, where all possible transitions are dipole allowed, see
Fig. 1. The energy differences of the |1-|2 and |2-|3
transitions are taken to be equal. Such structures have been
already studied for quantum interference and gain,
12
for con-
trolled coherent population trapping,
18
and for efficient sec-
ond harmonic generation.
35,36
Actually, this system can be
realized experimentally with only one laser frequency such
as that derived from a CO
2
laser. The fundamental CO
2
laser
frequency drives both the |1-|2 and |2-|3 transitions si-
multaneously and the |1-|3 transition is coupled by the
second harmonic frequency of the CO
2
laser, achieved by
frequency doubling in an appropriate infrared nonlinear crys-
tal, such as, for example, AgGaS
2
, AgGaSe
2
, GaSe, and
ZnGeP
2
.
37
The phase difference between the fundamental la-
ser field and its second harmonic is externally altered. The
small signal absorption or gain and dispersion spectra of a
weak probe propagating through such a quantum well struc-
ture are computed and are found to be crucially phase depen-
dent; therefore it can be phase controlled. The structure un-
der study combines simultaneously a closed-loop phase
control system and a two-color “fundamental plus the second
harmonic” phase control system.
We consider a n-doped three-level asymmetric quantum
well along the z direction with three equidistant dipole-
allowed conduction band ISBTs as depicted in Fig. 1. The
electron sheet density of the quantum well structure is such
FIG. 1. a Schematic of the energy level arrangement for the
asymmetric quantum wells considered in this paper. Subband levels
are labeled in ascending energy: |1, |2, and |3. There are
three possible optical transitions frequencies: |1 – |2
21
,
|2 – |3
32
, and |1 – |3
31
. We take
21
=
32
=
31
/ 2. The tran-
sitions |1–|2 and |2–|3 are driven by a coupling field with optical
frequency and the transition |1–|3 is coupled by a field with
optical frequency 2. b Schematic of the asymmetric conduction
band barrier arrangement to create the appropriate asymmetric
quantum well structure.
PHYSICAL REVIEW B 73, 233305 2006
1098-0121/2006/7323/2333054 ©2006 The American Physical Society 233305-1