Multiphoton coherent driving in harmonic and non-harmonic spin

systems

Irinel Chiorescu- Dept of Physics FSU & NHMFL

www.physics.fsu.edu

Graduate Program!www.physics.fsu.edu

Tallahassee, FL

Collaborators

postdoc: Sylvain Bertaina (moving to CNRS-Marseille, France)

grad students: Nick Groll, Lei Chen

Prof. Naresh Dalal

The EPR group at NHMFL Dr. J. van Tol Dr. S. Nellutla

Dept. of Chemistry, Florida State Univ.

Dept of Physics, Michigan State University Prof. M. Dykman

Funding: NSF-Career, DARPA, NHMFL, Alfred P. Sloan Foundation

Spin coherence with Mn spinsMn diluted in MgO single crystal

Spin Hamiltonian

H = a/6 [Sx4+Sy

4+Sz4- S(S+1)(3S2-1)/5] +gBH0·S-AS·I

g = 2.0025, a = 55.7 MHz, A = 244 MHz, S = I = 5/2

Room Temperature Spectroscopy Data

320 330 340 350 360 370

-400

0

400

mI=3/2 m

I=5/2m

I=1/2m

I=-1/2m

I=-3/2

Ab

sorb

tio

n D

eriv

ativ

e (a

.u.)

Magnetic field (mT)

Mn2+:MgO (1 1 1) T=300KH

0 || [0.9 0 -2] P=0.02mW

mI=-5/2

At low power, for a given mI, one see mostly the centralresonance -1/2 1/2

Spin levels, fixed mI :anisotropy non-harmonic

-5/2

5/2

-3/2

-1/2

3/21/2

mI=0, |mS|=1

Continuous wave multiphoton spectroscopy

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

-20

0

20

40

60

80

100

120

328 330 332423'

1"

1'

2'4

1" 2' 21' 3'4 53

5/2 3/2 1/2-1/2-3/2

low power hmw

=0.02 mT

high power hmw

=0.2 mT

3

2'

1'

1En

erg

y (

MH

z)

Static Field Detuning (mT)

1"

2

3'

4

5

-5/2 1

(a)

(b)

3'

2

1"1'2'

11'

2,2'

(c)

Ab

so

rpti

on

de

riva

tiv

e d

I / d

B (

a.u

.)Magnetic field [mT]

1"

3

2 dBm

x0.005

8 dBm

x0.05

14 dBm

23 dBm

20 dBm

H0 || [110], mI=-3/2

Room temperature Rabi oscillationsEPR measurement of <Sx> by Free Induction Decay method

Rabi frequency ~21 MHz

Rabi decay time ~200 ns

0.0 0.2 0.4 0.6 0.8 1.0-1.0

-0.5

0.0

0.5

1.0

<S

x> (

a.u.

)

Pulse length (s)

Rabi oscillations at room temperature

mI=-5/2, H0 || [100]

Multi-photon/multi-level spin control

Calculated dressed states diagrams. The level splittings give the Rabi frequency corresponding to each multi-photon coherent qubit nutation.

0.0

0.5

0.0

0.5

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.5

h = 0.22 mT

ARabi oscillations, T=30K

1-photon (1)

1-, 3-photon (1,3,3')

h = 1.1 mT

1-, 3-photon (1,3,3')

Pulse length (microseconds)

Ave

rag

e m

agn

etic

mo

men

t <

Sz>

h = 1.31 mT-1.0 -0.5 0.0 0.5 1.0

0

100

high MW power

(3)

Static Field Detuning (mT) Dre

ssed

Sta

tes

En

erg

y (M

Hz)

(1)(3')

low MW power

Rabi oscillations showing <Sz> as a function of MW pulse lengthfor different MW powers.

H0 || (1,0.8,1), mI=-3/2

4

2

Numerical SimulationsS. Bertaina (FSU & CNRS-Marseille, France)

0.0 0.5 1.0 1.50

20

40

60

3,3'

(b)

1

Rab

i fre

qu

ency

(M

Hz)

MW field amplitude hmw

(mT)0 0.8

FFT (a.u.)

Anisotropy and hyperfine terms << Zeeman term:- neglect forbidden transition, that is mI=0 indeed.- diagonalize H in a given mI subspace HmI

- external field good quantization axis , apply RFA: HmI static Hrot

- diagonalize Hrot energy diagram (dressed states picture)- time evolution of the density matrix time and temperature dependence of <Sx,y,z>

(Gaussian profile for the resonance)

Effect of anisotropy

-15 0 15 30 45 600

20

40

60

80

(deg)

Rab

i fre

qu

ency

(M

Hz) (a)

(b)

T = 40 Kh

mw = 1.34 mT

[100]

[010] H0

hmw

The compensation angle

0.0 0.2 0.4 0.6 0.8 0 20 40 600

1

2

Pulse length (s)

=45°

=33°

=45°

=33°

0.0

0.5

<S

z>

-0.5

=31° =31°

Frequency (MHz)

FF

T (

a.u

.)

(c)

Non-harmonic Harmonic

-15 0 15 30 45 600

20

40

60

80

(deg)

Rab

i fre

qu

ency

(M

Hz) (a)

(b)

T = 40 Kh

mw = 1.34 mT

[100]

[010] H0

hmw

hFR1 = 1/2 gBhmw (S(S+1)-Sz(Sz+1))

Rabi frequency between two consecutive levels, in a multi-level system:

Sz = -1/2 1/2 , for around 0°

Rabi frequency in a two level system:

hFRcomp = 1/2 gBhmw

FR1/FR

comp = 53.5 MHz / 18.07 MHz =2.96

At =comp : non-harmonic harmonic multi-level system with a 2-level system dynamics

0.0 0.5 1.0 1.50

10

20

30

40

-1 0 1

0

50

100

2

3

5

3'

1

3

(a)

T = 40KH

0 || [101]

1'

Rab

i F

req

uen

cy (

MH

z)

MW field amplitude hmw

(mT)

hmw =1.4 mT

3

2'

En

erg

y (M

Hz)

Static Field Detuning (mT)

3' 5

21 h

mw =0.02 mT

(b)

1'

Multi-photon Rabi oscillations

T=40K, H0 || [101] and mI=-3/2

comp at room temperature

0.0 0.2 0.4 0.6 0.8

-0.4

0.4RT, h

mw=0.52 mT

= 31° = 45°

<S

x>

Pulse length (s)

RT, hmw=0.52 mT: FR1/FR

comp = 21 MHz / 7 MHz =3

(to be compared with 2.96 at hmw=1.34 mT)