Control of the direction and rate of nuclear spin flips in InAs quantum dots using detuned optical pulse trains

0.48 MB·English

by  S. G. Carter

Control of the direction and rate of nuclear spin flips in InAs quantum dots using
detuned optical pulse trains
S. G. Carter,1 A. Shabaev,2 Sophia E. Economou,1 T. A. Kennedy,1 A. S. Bracker,1 and T. L. Reinecke1
1Naval Research Laboratory, Washington, DC 20375-5322, USA
2School of Computational Sciences, George Mason University, Fairfax, VA 22030, USA
(Dated: January 16, 2009)
Wefindthatdetuninganopticalpulsetrain fromelectronic transitionsinquantumdotscontrols
thedirectionofnuclearspinflips. Theopticalpulsetraingenerateselectronspinsthatprecessabout
anapplied magneticfield,with aspin componentparallel tothefieldonly fordetunedpulses. This
component leads to asymmetry in the nuclear spin flips, providing a way to produce a stable and
precise valueof thenuclearspin polarization. This effect is observed usingtwo-color, time-resolved
9
Faraday rotation and ellipticity.
0
0
PACSnumbers: 78.67.Hc,78.47.jc,72.25.Fe
2

n
6 Ja proSmpiinssinginqusaenmtuicmondbuitcst,orwitqhuasnptiunmcohdeortesnc(eQtDims)esaroef (a) z (yb) ulses S "(c#)$ "#%
a few microseconds [1, 2], controlled interactions with p
1 x
other QDs [3], and fast optical initialization and control QD Sx
] [4, 5, 6, 7]. A point of considerable current interest for probe !- !+
ph QDsasqubitsisthehyperfineinteractionwiththemany QD B ffielldd " #
(104-105) nuclei in the dot [8, 9, 10, 11, 12, 13, 14, 15,
-
t 16, 17, 18, 19, 20]. The nuclear spin configuration is
n
a typically random and varying in time. For a single QD
u measured over seconds, the nuclei sample many configu-
FIG.1: (coloronline)(a)Photoluminescenceofthequantum
q rations, changing the electron spin splitting through the
dots. The red vertical lines represent the pump and probe,
[
Overhauser effect. This leads to an apparent electron and the dashed vertical line represents an arbitrary QD en-
1 spindephasing time T∗ ofa few nanosecondsandanun- ergy. The actual detunings are much smaller than those dis-
2
v known spin splitting. played. (b) Experimental geometry showing spin precession.
3 (c)Electron-trionleveldiagram,showingthetwoelectronand
To overcome this problem, researchers have exam-
8 trion spin states and theallowed transitions. Single (double)
ined pumping nuclear spins into a narrow distribution
5 arrows are electron (hole) spins.
2 ofstates. Inelectricallydefinedquantumdots,repetitive
. gatemanipulationhasledtonarrowernuclearspindistri-
1
∗
butions andlengthening ofT [8]. Severalideasfor opti-
0 2
9 callypreparingnucleihavebeensuggested[9,10],witha clear spin dynamics. This optical control takes advan-
0 number of experiments demonstrating some controlover tage of recent progress in spin manipulation using both
: the nuclear spin polarization [11, 12, 13]. In particu- real excitation of electronic transitions [6, 21, 22, 23, 24]
v
i lar in Ref. [12], periodic excitation by an optical pulse andvirtualexcitationthatrotatesexistingspinpolariza-
X trainwasusedinanensembleofQDstovarythenuclear tions [7, 25, 26, 27, 28]. Using two-color, time-resolved
r spinfliprateasafunctionoftheelectronspinprecession Faraday rotation and ellipticity, we examine an ensem-
a
frequency. The underlying physics there is that sudden ble of QD spins at varying detunings from a pump pulse
changes in the electron spin state due to optical pulses train. The pulse train generates a spin polarization that
induce nuclear spin flips. Electron spins synchronized to precesses about an applied magnetic field and, for de-
a multiple of the laser repetition rate are not affected tuned QDs, also rotates the spins to give a significant
by the laserpulsesandhavemuchlowernuclearspinflip component parallel to the magnetic field. This parallel
ratesthanthosenotsynchronized. Withnoelectronspin component gives asymmetry in the spin flip rates. For
polarizationalongthemagneticfielddirection,thenuclei negative detuning, the asymmetry pushes electron spins
flipupordownwithequalprobability. Thus,thenuclear toward synchronized frequencies. For positive detuning,
polarizationtakesarandomwalk,asdoestheOverhauser thiscomponentpusheselectronspinsawayfromsynchro-
shifted electron spin precession frequency, until reaching nizedfrequencies,resultinginasymmetryinthespinam-
asynchronizedprecessionfrequencywithalowernuclear plitude versusQD detuning. These results open the way
spin flip rate. for precise control of the nuclear polarization and a bet-
terunderstandingoftheroleofthenucleiinelectronspin
In this Letter, we show that energy detuning of the
manipulation.
opticalpumping canbe usedtocontrolthe signandrate
of nuclear spin flips, leading to more deterministic nu- The experiments are performed on a sample consist-
2
ing of 20 layers of InAs QDs, grown by Molecular Beam )
d
Epitaxy through Stransky-Krastanovself-assembly. The ra40 (a) 60 W/cm2 80 (b) 600 W/cm2
$
QDs weregrownusing the In-flushtechnique [29],giving (30 60
y
aertarludnicmaetendsiopnysravmaridyinstgrufrcotumre1o0f-2h0eingmht.2W.5enfimndantdhaltata- pticit20 Ellipticity 40 Ellipticity
significant fraction (roughly 50%) of the QDs are singly elli10 20
chargedwithelectronscomingfromimpurities. Thepho- n/ 0 Rotation 0 Rotation
o
toluminescence (PL) of the QD sample at ∼5 K is given ati-10 -20
in Fig. 1(a), showing a broad spectrum due to inhomo- ot
R -400 0 400 800 -400 0 400 800
geneity, with a full-width at half-maximum (FWHM) of Delay (ps) Delay (ps)
∼50 meV. 0.3 S ! S "
timEel-ercetsroolnvesdpiFnardaydnaaymricostaatrioenm(eTaRsuFrRed) wanitdh etlwliop-tciociltoyr zation00..12 (c) QD = ±0.5 meV Szy! Sxx#
(TRFE). A circularly polarized pump laser spectrally ari 0
fixed at the center of the PL (see Fig. 1(a)) excites a pol-0.1
distribution of QDs with varying detunings δ from n -0.2
QD pi
the pump. A delayed, vertically polarized probe laser S-0.3
18 18.1 18.2 18.3 18.4 18.5
with variable detuning from the pump δprobe measures Precession frequency (GHz)
the pump-induced polarization rotation or ellipticity for
adistributionofQDsnearthe probephotonenergy. Ro-
FIG. 2: (color online) (a,b) Time-resolved Faraday rotation
tation (ellipticity) is due to the induced phase (ampli-
andellipticity forzeropump-probedetuning,takenatanav-
tude) difference between the σ+ and σ− components of eragepumpintensityof(a)∼60W/cm2and(b)∼600W/cm2
the probe. TRFR and TRFE are both sensitive to the forB=3T.Theellipticitycurvesareoffsetforclarity. (c)Cal-
spinpolarizationalongtheopticalaxisbuthavedifferent culatedcomponentsoftheelectronspinpolarization (labeled
spectral dependences. by direction and by the sign of detuning) as a function of
Both lasers are wavelength tunable mode-locked Ti- the spin precession frequency, for QDs detuned δQD = ±0.5
meVfrompumppulsesofareaπ. Completespinpolarization
tanium:Sapphire lasers operating at a repetition rate of corresponds to |S|=0.5.
81 MHz. The pump laser is set to a photon energy of
1.326 meV with a bandwidth of 0.6 meV, corresponding
to a Fourier-limited pulsewidth of 3 ps, and the probe
the spin precessionperiodis less than the recombination
laser has a bandwidth of 1.3 meV, corresponding to 1.4
time [21, 22, 23], which is the case in our experiment.
ps. The pump (probe) is focused onto the sample to a
diameter of ∼80 µm (∼50 µm), with a typical average The weaker oscillations observed for negative delays
probe intensity of ∼20 W/cm2. are due to mode-locking of spins [2]. If the individual
Figure2(a)displaysTRFRandtheTRFEforδprobe = electron spin coherence time T2 is longer than the pulse
0atanaveragepumpintensityof∼60W/cm2. Themag- repetition period TR, there is constructive interference
netic field is 3 T, perpendicular to the optical axis (see forspinsthatsatisfythephasesynchronizationcondition
Fig. 1(b)). The oscillating signal is the z component of (PSC) ω =2πN/TR, where N is an integer and ω is the
the electron spin, measured by the probe as it precesses spin precession frequency. The negative delay signal is
about the external magnetic field. The precession fre- fairly weak for low pump intensities, as in Fig. 2(a), and
quency is 18.2 GHz, corresponding to a |g | of 0.43. The stronger at higher pump intensities, as in Fig. 2(b). By
e
decay time of 450 ps is due to inhomogeneity in ge, con- measuringmode-lockingforseveraldifferentvaluesofTR,
firmed by our magnetic field studies. The TRFR shows we estimate T2 at100-200ns for this sample, anorderof
similar behavior to the TRFE, but with a weakersignal. magnitude smaller than the T2 measured in Ref. [2]. We
TRFRandTRFEmeasuretherealandimaginarypartof assign this difference to the smaller volume of our QDs
the susceptibility, i.e., dispersion and absorption respec- [20] compared to those of Ref. [2].
tively. These are generally known to be odd and even Surprisingly, the TRFR signal is comparable to the
functions of the detuning from the transition. Thus, at TRFE signal at the higher pump intensity (Fig. 2(b)),
δprobe =0,theTRFRshouldbenearzero,andtheTRFE even though the TRFR is expected to be near zero for
should be at a maximum. δ =0. This result is the first hint of physics beyond
probe
The electron spin polarization is generated by optical simplypumping electronsintothe|↓istate throughreal
pumping through the trion state. As shown in Fig. 1(c), transitions. For δ 6= 0, the pulse train also rotates
QD
where the spinstates areshowninthe z-basis(alongthe spins about the optical axis through virtual transitions
opticalaxis), σ+ lightdepletes the |↑ie spinstate, leav- to the trion. As a result, in addition to the spin com-
ing behind excess population in the | ↓i state. The gen- ponents perpendicular to the magnetic field, a parallel
erated polarization persists after trion recombination if or antiparallel component also will be generated. Con-
3
sider for example a spin oriented along −zˆ by an initial meV for the ellipticity and ∼0.7 meV for the rotationat
pulse, which then precesses until the next pulse. If the the highest pump intensity are more interesting. Cer-
precession frequency is not at a PSC, there will be an tainly these shifts explain the large rotation signal ob-
S component just before the next pulse, which will be servedathighpumpintensitiesforδ =0inFig.2(b).
y probe
partially rotated into the xˆ direction by the virtual pro- We attribute the spectral shifts to different nuclear dy-
cess. Figure 2(c) displays the calculated steady state namics for positive and negative δ .
QD
electron spin vector components right after a pulse as
functions of the spin precession frequency. The troughs
in the z-component of the spin vector, Sz correspond to Hz) 1
frequencies meeting the PSC. The sign of the detuning e (
determines the sign of the rotation angle [26], and thus at
r
the sign of S , without affecting S or S . p 0.5
x z y n fli (a) www
ip "
) 15 30E S 0
amp. (rad! 1050 (a) 63690000000 (b) 122505llipticity am y of states 12 (b) !!!QQQDDD>=<000
otation -1-50 510!p. (ra Densit 018 18PP.rr1eecceessss1iioo8.nn2 ffrreeqquu1ee8nn.3ccyy ((GGHH1zz8)).4 18.5
R-15 0 d)
100
) (c) 0.3 (d) C
Calc. rotation (a.u.-101 -4 -2 0 2 4 011...704- 4 -2 0 2 4 0123alc. ellipticity (a.u.) etim!!<0(QDc) !!=0(QDd) !!>0(QDe) 111000 213
Probe detuning (meV) 1 0 1 1 0 1 1 0 1
Nuclear!polarization!n/N(%)
FIG. 3: (color online) (a,b) Positive delay amplitude of the
experimental(a)TRFRand(b)TRFEasafunctionofprobe FIG. 4: (color online) (a) Calculated nuclear spin flip rates
detuning from the pump for a series of pump intensities (in as afunction of electron spin precession frequencyfor δQD =
W/cm2). (c,d) Theoretical calculation of the positive delay −0.5 meV and π-pulses. (b) Calculated steady state density
amplitude of (c) rotation and (d) ellipticity for a series of ofstatesasafunctionofelectronspinprecessionfrequencyfor
pulse areas (shown in theinsets). δQD =−0.8,0,+0.8meVandπ-pulses. FornegativeδQD the
QDs are focused toward the PSCs more efficiently than for
The nuclear dynamics are significantly changed by a theδQD =0case, whilefor positiveδQD theQDsarepushed
away from the PSCs. (c,d,e) Time evolution of P(n) for (c)
nonzero Sx since the nuclear spin flip rates w± are pro- δQD <0, (d) δQD =0, and (e) δQD >0, each using π-pulses.
portionalto(1±2Sx)[30]. WhenSx 6=0thenuclearspin The logarithmic scale for P(n) is cut off for P(n)<10−3.
flip rate from spin up to down, w−, is different from the
rate to flip from down to up, w+ [31]. Since Sx depends
on δQD, we expect some manifestation of the changing Our calculations, which include the feedback effect of
nucleardynamicswhendifferentenergyQDsareprobed. thenucleiontheelectronspinprecessionfrequency,qual-
ThemeasuredFaradayrotationandellipticityareplot- itatively reproduce these shifts, as shown in Fig. 3(c,d).
ted versus δ in Fig. 3(a) and 3(b) respectively, for a To calculate the optical response from the inhomoge-
probe
series of pump intensities. The rotation and ellipticity neousQD ensemble we firstfind the steadystate expres-
are very nearly the expected odd and even functions of sions for the spin components. We use pulse shapes for
δ atthelowestpumpintensity,60W/cm2,indicating the pump that provide analyticalsolutions for any pulse
probe
the distribution of spin-polarized QDs is symmetric and strength and detuning. Our calculations have been done
spectrally narrow. With increasing pump intensity, the for hyperbolic secant pulses [32] and for square pulses,
spectral features in Fig. 3(a,b) are broader and clearly andtheygivequalitativelythesameresults. Thenuclear
shift toward lower probe energies. The broadening can spin flip rates are functions of the precession frequency
be explainedby higherpumpintensitiespolarizingwider ω,the RabifrequencyΩ,thedetuning δ ,andthespin
QD
spectraldistributionsofQDs. Thespectralshiftsof∼0.4 vectorcomponents,whicharealsofunctionsofω,Ω,and
4
δ [12]: tuned pulses we can control the effects of the hyperfine
QD
interaction of the electron with the nuclear spin. This
W(Ω,δ )[1+2S ]
w± ∝ 2T QD ω2 z [1±2Sx], (1) work provides an additional handle toward optical con-
R trol of the nuclear QD spins.
whereW isthetransitionprobabilityoftheallowedelec-
This work is supported by the US Office of Naval Re-
tron to trion transition. The rates are plotted in Fig.
search. One of us (S.E.E.) is an NRC/NRL Research
4(a) as functions of the precession frequency. Using Eq.
Associate.
(1),wesolvenumericallyforthesteadystatenuclearpo-
larization probability distribution, P(n), where n is the
number of spin up nuclei minus the number spin down.
ThetotalnumberofnucleiN isestimatedat20,000from
the size of our QDs. The time evolution of P(n) is dis-
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5
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