Pumped spin-current and shot noise spectra in a single quantum dot

0.21 MB·English

by  Bing Dong

Pumped spin-current and shot noise spectra in a single quantum dot
Bing Dong1,2, H.L. Cui1,3, and X.L. Lei2
1Department of Physics and Engineering Physics,
Stevens Institute of Technology, Hoboken, New Jersey 07030
2Department of Physics, Shanghai Jiaotong University, 1954 Huashan Road, Shanghai 200030, China
5 3School of Optoelectronics Information Science and Technology, Yantai University, Yantai, Shandong, China
0
0 We exploit the pumped spin-current and current noise spectra under equilibrium condition in
2 a single quantum dot connected to two normal leads, as an electrical scheme for detection of the

n electron spin resonance (ESR) and decoherence. Wepropose spin-resolved quantumrate equations
a withcorrelation functionsin Laplace-spacefor theanalytical derivationofthezero-frequencyatuo-
J and cross-shot noise spectra of charge- and spin-current. Our results show that in the strong

5 Coulomb blockade regime, ESR-induced spin flip generates a finite spin-current and the quantum
2 partition noises in theabsence of net charge transport. Moreover, spin shot noise is closely related
tothe magnetic Rabi frequency and decoherence and would be a sensitive tool to measure them.

]
l
l PACSnumbers: 72.70.+m,73.23.Hk,73.50.Td,85.35.-p
a
h
-
Introduction—There have been extensive investiga-
s
(cid:0)(cid:1)
e tions focused on electron spin detection and measure- (cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)
(cid:0)(cid:1)
m (cid:0)(cid:1)
ment via charge transport in mesoscopic quantum dot (cid:0)(cid:1)
. (QD) system,[1, 2, 3] which is motivated from the fact (cid:0)(cid:1)
t (cid:0)(cid:1)
a thateasypreparationandmanipulationofelectronspins, (cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:1)
m (cid:0)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)
as well as the remarkably long spin coherence time, pro- (cid:0)(cid:1)
[cond- vigsrnpeoidfpivoneoerrrmtdtnheyaeedndtwiabonmaynoyidtcpfisroro.oernccaRletypseospcbpilenyitncgicat.t[lath4yil,e]oinnIacnsjhepiactnuhtrrigesoepesneisnflwpstoyiriwntoshtn,ceoiumbcursutsrta,egnnteardtnlasehqnoruasabpsatiyonobrtnettuehmoinesf (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)µ(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)L(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:1)Γ(cid:0)(cid:1)L(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)εε(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)Rr(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)f (cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)U(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)Γ(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)R(cid:0)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)µ(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)R(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)
3 a net charge current.[5] Theoretically, a spin source de- (cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1) (cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)
(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1) (cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)
v vicehasalsobeenproposedtocarrypurespinflowbased
4 on electron spin resonance (ESR) in a QD-lead system FIG. 1: Schematic view for theQD-based spin battery.
6
withsizableZeemansplitting.[6,7]Moreover,bothauto-
0
and cross-correlation noise spectra of spin-current have
4
larlyto the constantfield B withthe frequency Ω nearly
0 been studied for this QD-based spin battery.[8]
equal to ∆ can pump electron to the higher level where
4
0 However, Coulomb blockade (CB) effect on this QD itsspinisflipped,thenthespin-downelectroncantunnel
/ spinbatteryneeds investigation,sinceCB effectisanes- outto the leads. Becausethe twocurrentswith opposite
t
a sential feature of transport through a QD. More impor- directions have different spin orientations, spin-currents
m
tantly,thespinconfigurationoftheconfinedelectronson are established in both leads with equal values. If the
- QD is apparently affected by CB effect, which directly Coulomb interaction in the QD is strong enough to pro-
d
determine the efficiency of this device. As well, these hibit the double occupation, no more electrons can en-
n
o previous studies also neglected the inevitable spin deco- ter the QD before the spin-down electron exits. As a
c herence due to coupling of the single spin with environ- result, the number of electrons exiting from the QD is
v: ment. Therefore,it is the purpose of this paper to study equal to that of electrons entering the QD, namely, the
i this ERS-pumped spin-current and its fluctuations for a chargecurrentsexactlycancelouteachother. Otherwise,
X
QD connected with two normal leads in the strong CB in the case ǫ +U < µ the ESR pumping will generate
↑
r
regime at zero temperature. The setup is schematically both spin-current and charge-current. Note that both
a
depicted in Fig. 1: The single electron levels in the dot leads have contributions to the spin-current of one lead,
aresplitbyanexternalmagneticfieldB,ǫ −ǫ =g µ B causingthecorrelationofspin-currentsindifferentleads,
↓ ↑ z B
(= ∆ Zeeman energy), where g is the effective electron whichprovidespossibilityofstudyingcross-correlationof
z
g-factor in the z direction and µ is the Bohr magne- spin currents without bias voltage.[9]
B
ton. The gate voltage controls the chemical potentials Theoretical formalism—We write the Hamiltonian of
µ of two leads located between the two split levels and the ESR-induced spin battery under consideration as:
no bias voltage is applied to the two leads. After a spin-
up electron tunnels into the QD, an oscillating magnetic H = ǫ c† c + ǫ c† c +Un n
ηkσ ηkσ ηkσ σ dσ dσ d↑ d↓
fieldB (t)=(B cosΩt, B sinΩt)appliedperpendicu- X X
rf rf rf η,k,σ σ
2
+ X(Vηc†ηkσcdσ+H.c.)+Hrf(t), (1) +iδESRρ↑(↓mmLL↓↑,,mmRR↓↑)−[12(ΓL↓+ΓR↓)+ T1 ]ρ↑(↓mmLL↓↑,,mmRR↓↑), (3d)
η,k,σ 2
where c†ηkσ (cηkσ) andc†dσ (cdσ) arethe creation(annihi- and the normalization relation ρ00 + σρσσ = 1. The
lation)operatorsfor electronswith momentumk, spin-σ (mL↑,mR↑) P
equation of motion for ρ mL↓,mR↓ can be obtained by
and energy ǫ in the lead η (= L,R) and for a spin-σ ↓↑
ηkσ
implementing complex conjugate on Eq. (3d). In these
electron on the QD, respectively. The third term de-
equations, δ = ∆ − Ω is the ESR detuning and
scribes the Coulomb interaction among electrons on the ESR
QD. ndσ =c†dσcdσ is the occupation operator in the QD. Γplηiσng=b2eπtwPeekn|Vthηe|2Qδ(Dω−anǫηdktσh)edleenaodteηsitnhveoslvtrinenggstphinofσc.oIun-
The fourth term represents the tunneling coupling be-
widebandlimit,thesetunnelingamplitudesareindepen-
tween the QD and the reservoirs. The last term H (t)
rf
dentofenergyandforsimplicitywesetΓ =Γ =Γ/2.
describesthecouplingbetweenthespinstatesduetothe η↑ η↓
Furthermore,wedescribethecouplingofsinglespinwith
rotating field B (t) and can be written, in the rotating
rf
the environment in a phenomenological way via intro-
wave approximation (RWA), as
ducing two time scales: the spin relaxation time T of
1
H (t)=R c† c eiΩt+c† c e−iΩt , (2) an excited spin state into the thermal equilibrium, and
rf rf d↑ d↓ d↓ d↑
(cid:0) (cid:1) the spin decoherence time T2 relatedto the loss of phase
withtheESRRabifrequencyRrf =g⊥µBBrf/2,withthe coherence of the spin superposition state. The measure-
g-factor g⊥ and the amplitude of the rf field Brf. ment of T2 in QDs is currently active topic because it
Here, in order to anticipate the CB and the intrin- is the limit time scale for coherent spin manipulation
sic spin relaxation, we utilize the quantum rate equa- and thus quantum information processing. In typical
tions for the system density matrix elements: ρ00 and GaAsQD,Γ=8µeV,correspondingtoatunnelingtime
ρσσ describe the occupation probability in the QD be- τ ∼ Γ−1 = 0.5 ns. To observe single- and multi-photon
ing, respectively, unoccupied and spin-σ states, and effects in tunneling (nonadiabatic regime), it must re-
the off-diagonal term ρ denotes coherent superpo- quirethespinflippingtimeT <τ. IfonetakesB =1T,
↑↓(↓↑) Ω
sition of the two coupled spin states in the QD.[10] The the Zeeman energy is ∆ = 26 µeV which determine the
doubly-occupied state is prohibited due to the infinite optimal driving frequency Ω = 13π GHz and the cor-
Coulomb interaction U → ∞. Here we focus our in- responding T = 0.15 ns. These proposed spin-device
Ω
terest on the nonadiabatic pumping where the photo- parameters can be easily realized by present technology.
assisted resonance is achieved and neglect cotunneling
Recently, T in a single QD was probed to be an or-
1
processes. For the purpose of evaluating the noise spec- der of microsecond via transport experiment,[11] which
trum, we introduce the spin-resolved (in both termi-
is notably longer than other time scales T ≫T , τ, T .
(mL↑,mR↑) 1 2 Ω
nals) density matrices ρ mL↓,mR↓ (t), meaning that the Hence it is a good approximation to assume T1 → ∞
ab
QD is on the electronic state |ai (a = b = 0, ↑, ↓) or in the following calculation. Consequently, one recovers
on quantum superposition state (a 6= b) at time t to- theusualquantumrateequationsforthereduceddensity
getherwithmL↑ (mR↑)spin-upelectronsandmL↓(mR↓) matrixelementsρab(t)forasingleQDwithspincoupling:
spin-down electrons in the left (right) lead. Obviously, ρ˙(t)=(ρ˙00,ρ˙↑↑,ρ˙↓↓,ρ˙↑↓,ρ˙↓↑)=Mρ(t) with[3, 10]
(mL↑,mR↑)
ρ (t) = ρ mL↓,mR↓ (t) and the quantum rate
ab PmmLL↓↑,,mmRR↓↑ ab −Γ↑ 0 Γ↓ 0 0
equations for these spin-resolved density matrices in the  Γ 0 0 iR −iR 
↑ rf rf
rotating frame with respect to Ω are M= 0 0 −Γ −iR iR ,
 ↓ rf rf 
(mL↑,mR↑) ( mL↑,mR↑ ) ( mL↑,mR↑ )  0 iRrf −iRrf −Γ↓V +iδESR 0 
ρ˙00mL↓,mR↓ = ΓL↓ρ↓↓mL↓−1,mR↓ +ΓR↓ρ↓↓mL↓,mR↓−1  0 −iRrf iRrf 0 −Γ↓V +iδESR 
(mL↑,mR↑) (4)
−(ΓL↑+ΓR↑)ρ00mL↓,mR↓ , (3a) and V = 1 + 1 .
(mL↑,mR↑) (mL↑+1,mR↑) (mL↑,mR↑+1) 2 Γ↓T2
ρ˙↑↑mL↓,mR↓ = ΓL↑ρ00mL↓,mR↓ +ΓR↑ρ00mL↓,mR↓ Spin-current—The spin-related currents Iησ can be
1 (mL↑,mR↑) 1 (mL↑,mR↑) evaluatedbythetimechangerateofspin-σelectronnum-
+ ρ mL↓,mR↓ − ρ mL↓,mR↓ ber in the η lead
2T ↓↓ 2T ↑↑
1 1
(mL↑,mR↑) (mL↑,mR↑)
+iRrf(ρ↑↓mL↓,mR↓ −ρ↓↑mL↓,mR↓ ), (3b) I = eN˙ =e d m P(t) , (5)
(mL↑,mR↑) (mL↑,mR↑) 1 (mL↑,mR↑) ησ ησ dt ησ t→∞
ρ˙↓↓mL↓,mR↓ = −(ΓL↓+ΓR↓)ρ↓↓mL↓,mR↓ + 2T ρ↑↑mL↓,mR↓ mmLLX↓↑,,mmRR↓↑ (cid:12)(cid:12)
1
1 (mL↑,mR↑) (mL↑,mR↑) (mL↑,mR↑) (mL↑,mR↑) (mL↑,mR↑) (mL↑,mR↑)
− ρ mL↓,mR↓ +iR (ρ mL↓,mR↓ −ρ mL↓,mR↓ ), (3c) P(t) = ρ mL↓,mR↓ (t)+ρ mL↓,mR↓ (t)+ρ mL↓,mR↓ (t).
2T ↓↓ rf ↑↓ ↓↑ 00 ↑↑ ↓↓
1
(mL↑,mR↑) (mL↑,mR↑) (mL↑,mR↑)
ρ˙ mL↓,mR↓ = iR (ρ mL↓,mR↓ −ρ mL↓,mR↓ ) Inparticular,usingEqs.(3)wefindI =−eΓ ρ and
↑↓ rf ↑↑ ↓↓ L↑ L↑ 00
3

0.4 0.330 meaning anti-bunching of the wavepacket. Interestingly,
Γ = 0.5 (a) Γ = 0.5 (b)
0.3 δESR=0 Rrf=2.0Γ 0.325 mthuecchrosstsu-dcioersrehlaavtieonbecehnandgeevsotitesdstiognfi.[n1d4]aHseyrsetewme wwohuerlde
Γ'/Γ 0.320 like to address that the spin-resolved CC is more useful
sΓI/e 0.2 0.40.0 0I.5s 1.0 00..331105 I/eΓs twPoaauvdeleipseacxcrikcbleuetsiewolneitchtprrooinnpcpicoposlreirteealnasdtpiiononns,lyibseruceaflnueincsfletsuteuhnnecaeemdlebcbitgyruootnhuiecs
0.2
0.1 ΓI/e0.0 Ic δ1E/TSR2==00 100/..25TΓΓ2=0. 0.305 ienvfaolrumataitnigonthaebocuhtartgheeainndtersapcitnioCn.CFfroormthtehepuqrupaonsteumof
-0.2 1.0Γ
0.0 0.300 rate equations (3), we extend the MacDonald’s formula
0.0 0.5 1.0 1.5 2.0-1.0 -0.5 0.0 0.5 1.0
for the spin-resolved situation:[15]
R /Γ δ /Γ
rf ESR ∞ d
FIG. 2: The spin-current vs (a) strength and (b) detuning Sησησ′′(ω) = 2ωe2Z0 dtsin(ωt)dtnmLX↑,mR↑ mησmη′σ′
of the driving field for different spin decoherence time. In- mL↓,mR↓
set in (a): Overviewof′thecharge- and spin-currentwith the ×P(t)−t2IησIη′σ′/e2 . (10)
Coulomb correlation Γ. Thecalculated strengthoftheoscil- o
lation magnetic field corresponds to 0∼1 T.
Specially, the zero-frequency shot noise spectrum is
d t2
IL↓ =eΓL↓ρ↓↓. The2stRa2tiVon+arδy2solu+tioΓn2Vo2f Eqs. (3) is: Sησησ′′(0)=2e2dtnmmLLX↓↑,,mmRR↓↑ mησmη′σ′P(t)−e2IησIη′σ′o(cid:12)(cid:12)t→∞.
ρ = rf ESR , (6) (11)
↑↑
Ξ
The auto- and cross-noise spectra of the charge-current
2R2V
ρ = rf , (7) andspin-currentcanbe obtainedfromthesecorrelations
↓↓
Ξ Sσσ′: Sc/s =S↑↑ +S↓↓ ±S↑↓ ±S↓↑ .
R [iΓV −δ ] ηη′ ηη′ ηη′ ηη′ ηη′ ηη′
ρ = rf ESR , (8) In order to evaluate these correlations, we introduce
↑↓
Ξ the following generating functions:
withΞ=6Rr2fV+Γ2V2+δE2SR. Obviously,thestationary (mL↑,mR↑)
charge-current is exactly zero Ic = I +I = 0, while Gab(t)= m ρ mL↓,mR↓ (t). (12)
η η↑ η↓ ησ ησ ab
the spin-current is mLX↑,mR↑
mL↓,mR↓
2R2ΓV
Is =I −I =e rf , Is =−Is. (9) With the help of Eqs. (3), all noise spectra are therefore
L L↓ L↑ Ξ R L relevant with these auxiliary functions and ρ (t) as:
ab
Explicitly, the spin-current is proportional to the exci-
ttahtisioEnSpRo-wbaers,edwshpicinhbisatctoenrys.isAtenndtiwt’isthamthpelitpurdoetoetxyhpiebiotsf Sησ2ησe′′2(0) = 12Γσδσσ′[δηη′(ρ00(t)δσ↑+ρ↓↓(t)δσ↓)
(cid:8) 1
a saturation behavior with increasing driving field as a + (G↓η↓′′σ(t)δσ↓−G0η0′′σ(t)δσ↑)]+δσσ¯′[2Γ↓G↓η↓↑(t)
consequence ofthe nonlinear photon-absorptionof a sin- Xη′′
gle spin [Fig. 2(a)]. The saturated value is eΓ/3 inde- 1 2t
pendent on the decoherence time T and detuning δ . −2Γ↑G0η0′↓(t)]− e2IησIη′σ′ t→∞. (13)
2 ESR (cid:9)(cid:12)
Figure 2(b) shows that the detailed dependence of the (cid:12)
On the other hand, using Eqs.(3), the equations of mo-
spin-current on the driving frequency is determined by tion for G (t) is explicitly obtained in matrix form:
ησ
the spin decoherence time T2. In the inset of Fig. 2(a), G˙ (t)=MG (t)+G ρ(t) with
we show that nonzero charge-current is also pumped by ησ ησ ησ
the driving field unless the double occupation is prohib- 0 0 Γ δ 0 0
η↓ σ↓
ited owing to the strong charging effect Γ′ = 0.[12] This  −Γ δ 0 0 0 0
η↑ σ↑
verifies our statement in the introduction. G = 0 0 0 0 0 . (14)
ησ  
Spin shot noise—Recently nonequilibrium quantum  0 0 0 0 0
 
shot noise is another current active subject in meso-  0 0 0 0 0
 
scopic physics, because the current correlation (CC) is
Applying Laplace transform to these equations yields
inherently related to the quantization of electron charge
and thus give unique information about electronic cor- G (s)=(sI−M)−1G ρ(s), (15)
ησ ησ
relation, which cannot be obtained by probing the con-
ductance only.[13] For instance, the cross-correlationfor where ρ(s) is readily obtained by performing Laplace
charge-current (the correlation between different termi- transform on its equations of motion and the normal-
nals) is negative for a normal single-electron transistor, ization relation. Due to inherent long-time stability of
4

0.8 10/.2TΓ2=0 δESR=0 sthheotsnpoinis-ecuisrrmenotreansednstihteivcehtaorgtheeshspoitnndoeicseo.heTrehnicsectohualnd
0.5Γ LL
0.6 1.0Γ provide a way to measure the spin decoherence time T .
1/T=0 2
2 In summary, we have presented a generic method for
Γ 0.4
2e analytical calculation of the atuo- and cross-shot noise
2 LL
sS/ 0.2 spectraofcharge-andspin-currentin anESR-basedsin-
gle QD system. We found that in the strong CB regime,
LR
0.0 LR (a) R10..r05f=ΓΓ2.0Γ (b) indeed ESR pumping generates a finite spin-current and
-0.2 0.25Γ quantum partition noises in the absence of net charge
0.0 0.5 1.0 1.5 2.0 -0.5 0.0 0.5 1.0 transport. And the spin shot noises display complicated
behaviorsdependingonthepumpingparametersandthe
R /Γ δ /Γ
rf ESR spindecoherencetime. Themeasurementofspin-current
andshotnoise providesa scheme forthe Rabioscillation
FIG. 3: The zero-frequency auto- and cross-correlations of and spin decoherence detections in the QD system.
spin-currentvs(a)strengthand(b)detuningofdrivingfield.
BDandHLC aresupportedbythe DURINT Program
administered by the US Army Research Office. XLL is
supported by Major Projects of National Natural Sci-
the physics system under investigation, all real parts of ence Foundation of China, the Special Founds for Major
nonzero poles of ρ(s) and G(s) are negative definite. State Basic Research Project and the Shanghai Munici-
Consequently, the large-t behavior of the auxiliary func- pal Commission of Science and Technology.
tionsisentirelydeterminedbythedivergenttermsofthe
partial fractionexpansions of ρ(s) and G (s) at s→0.
ησ
Resolving both G (s) and ρ(s) into the partial frac-
ησ
tion expansion forms and performing inverse Laplace
[1] H.A. Engel and D. Loss, Phys. Rev. Lett. 86, 4648
transform,wecaneventuallyderivetheanalyticalexpres-
(2001); Phys.Rev.B 65, 195321 (2002).
sions for these large-t asymptotic correlations. Surpris-
[2] A.V. Balatsky and I. Martin, cond-mat/0112407; D.
ingly,wefindthezero-frequencychargeshotnoisesbeing
Mozyrsky,L.Fedichkin,S.A.Gurvitz,andG.P.Berman,
proportional to the spin-current SLcL = −SLcR = e2|ILs|, Phys.Rev.B66,161313(2002); J.X.ZhuandA.V.Bal-
whichmanifeststhatpumpingprocessesdogenerateshot atsky, Phys.Rev.Lett. 89, 286802 (2002).
noise even in the absence of net charge-current. This [3] I.Martin,D.Mozyrsky,andH.W.Jiang,Phys.Rev.Lett.
feature is underlying analog of the quantum partition 90, 18301 (2003).
[4] G.A. Prinz, Science 282, 1660 (1998); S.A. Wolf, D.D.
noise of photo-excited electron-hole pairs demonstrated
Awschalom, R.A. Buhrman, J.M. Daughton, S.V. Mol-
intherecentexperiment.[16]Spin-upandspin-downelec-
nar,M.L.Roukes,A.Y.Chtchelkanova,D.M.Treger,Sci-
trons in this spin battery are dissociated by tunneling ence 294, 1488 (2001).
eventsinthe presenceofpumping fieldbutwithoutbias: [5] M.J.Stevens,A.L.Smirl,R.D.R.Bhat,A.Najmaie,J.E.
spin-upelectronsinjectintotheQD,butspin-downelec- Sipe, and H.M. van Driel, Phys. Rev. Lett. 90, 136603
trons flow off in an opposite direction. As expected, the (2003); J. Hu¨bner, W.W. Ru¨hle, M. Klude, D. Hommel,
cross-correlation of the charge noise is always negative R.D.R. Bhat, J.E. Sipe, and H.M. van Driel, Phys. Rev.
Lett. 90, 216601 (2003).
definite, showing anti-bunching statistics, but it has the
[6] B.G. Wang, J. Wang, and H. Guo, Phys. Rev. B 67,
same magnitude with the auto-correlationof the charge-
92408 (2003).
currentoriginatedfromtheconservationlawofcharge.[8] [7] P. Zhang,Q.K.Xue,and X.C.Xie, Phys.Rev.Lett. 91,
However, the situation is very different for the zero- 196602 (2003).
frequency spin shot noise, as shown in Fig. 3. The auto- [8] B.G. Wang, J. Wang, and H. Guo, cond-mat/0305066
correlation of the spin-current is surely positive definite, (2003).
[9] O. Sauret and D. Feinberg, Phys. Rev. Lett. 92, 106601
while the cross-correlation is either positive or negative
(2004).
dependingonanumberofparameters: the pumpingam-
[10] S.A. Gurvitz and Ya.S. Prager, Phys. Rev. B 53, 15932
plitude R , the detuning δ , and the decoherence T .
rf ESR 2 (1996); B. Dong, H.L. Cui, and X.L. Lei, Phys. Rev. B
For small decoherence rates, the spin cross-correlation 69 35324 (2004).
experiences the changeof signwith increasingexcitation [11] T. Fujisawa, Y.Tokura,and Y.Hirayama, Phys.Rev.B
R at resonant pumping δ = 0. Interestingly, this 63 81304(R) (2001).
rf ESR
cross-correlationisalwayspositive(1)atlargeexcitation [12] Extension of zero-temperature spin-resolved quantum
rate equations and current formula are easily achieved
R >Γ regardless of decoherence T [Fig. 3(a)] or (2) if
rf 2 for considering the doubly occupied state. See Ref. 10.
apartawayfromquantumresonance[Fig.3(b)]. Thesig- ′
Charging effect is modeled by tunnelingrate Γ.
nificant role of decoherence is to evidently reduce these [13] Ya.M. Blanter and M. Bu¨ttiker, Phys. Rep. 336, 1
noise spectra and even to eliminate the change of sign (2000).
in the spin cross-correlation. It is addressed that spin [14] P. Samuelsson and M. Bu¨ttiker, Phys. Rev. Lett. 89,
5
46601 (2002); F. Taddei and R. Fazio, Phys. Rev. B 65, Chen and C.S. Ting, Phys. Rev.B 46, 4714 (1992).
134522(2002);D.S´anchez,R.L´opez,P.Samuelsson,and [16] L.H. Reydellet, P. Roche, D.C. Glattli, B. Etienne, and
M. Bu¨ttiker, Phys.Rev.B 68, 214501 (2003). Y. Jin, Phys. Rev.Lett. 90, 176803 (2003).
[15] D.K.C.MacDonald,Rep.Prog.Phys.12,56(1948);L.Y.