Dynamical Casimir emission Dynamical Casimir emission and back-action effects and back-action effects

in optically modulated microcavitiesin optically modulated microcavities

Iacopo CarusottoINO-CNR BEC Center and Università di Trento, Italy

In collaboration with:● Cristiano Ciuti and Simone De Liberato (MPQ, Université Paris-Diderot)● Dario Gerace ( Università di Pavia )

International Workshop on Dynamical Casimir Effect, Padova, June 6-8, 2011

The dynamical Casimir effect

Mechanically shake it very fast

Take an optical cavityin the e.m. vacuum state

Beware when you open it again: (a few) photons may burn you !!

Mechanism of photon generation:● theoretically well understood● first experimental evidences now available

Open questions:● back-action of DCE emission onto mirrors● how does one feel the DCE photons while mechanically shaking the cavity?

How strong is the back-action effect?

Half-space slab of refractive index n and mass M Mechanically oscillating at frequency Ω Prediction for the dissipated energy within 1D scalar model:

(from Barton and Eberlein, Ann. Phys. 227, 222 (1993))

➔ value is ridiculously small➔ very little hope of experimental observation

Q−1=

2Eosc

dEdiss

dt=1

6 n−1n

2 ℏMc2

n

Ω

What matters is optical length of cavity Lopt

= n L

Mechanical oscillation of mirrors ↔ Modulation of refractive index

Emission strongest on resonance with cavity modes: Ω = ωi + ω

j

All-optical Dynamical Casimir effect

Ω Ω

n(t)=n0+ dn cos(Ωt)

V. V. Dodonov et al., PRA 47, 4422 (1993); Yablonovitch, PRL. 62, 1742 (1989); Law, PRA 49, 433 (1994).

Photo-excitation of carriers in mirrorBraggio et al., EPL 70 754 (2005)

χ(3) nonlinear medium pumped by ultrashort pulsed laser

IC and D. Faccio, in preparation

DCE vs. optical parametric oscillatorDezael and Lambrecht, EPL 89 14001 (2010)

Time-dependent EIT in atomic Mott insulatorIC et al., PRA77, 063621 2008

Circuit QED: effective cavity length modulated via external B on SQUID

Wilson et al.,, PRL 105, 233907 (2010); arXiv:1105.4714

Physical implementations

θ } Doped QWs

Conduction band

1

2

Energy

mirror

mirror

cavity modetuned in the

far-IR,resonant withintersubbandtransition indoped QW doping provides electrons

in lowest subband ofconduction band

Intersubband transition in doped quantum wellsembedded in a semiconductor microcavity

D. Dini et al., PRL 90, 116401 (2003)

L. Sapienza et al., PRL 100, 136806 (2008)

Upper Polariton

Ultra-strong coupling regime

For each value of in-plane wavevector k:● one cavity-photon state coupled to

one matter excitation● bosonic mixed polaritonic excitations

(a kind of dressed photons)● strong-coupling Ω

R > Γ

● ultra-strong coupling ΩR~ ω

0

Theory: C. Ciuti, G. Bastard, IC, PRB 72, 115303 (2005)

(Bosonized) system Hamiltonian

System Hamiltonian quadratic in bosonic field operators:● a

q → cavity photon; b

q → intersubband collective excitation

● Rabi frequency ΩR couples cavity photon ↔ intersubband excitation

● if ΩR comparable to

ω

cav, ω

12 → anti-RWA terms relevant,

create/destroy pairs of excitations● ground state contains finite number of excitations

C. Ciuti, G. Bastard, IC, PRB 72, 115303 (2005)

Ground state of system: polaritonic vacuum

contains (virtual) photons and intersubband excitations

The non-trivial vacuum state

Hamiltonian diagonalized via Bogoliubov transformation

New bosonic operators:

C. Ciuti, G. Bastard, IC, PRB 72, 115303 (2005); C. Ciuti, IC, PRA 74, 033811 (2006)

Extra photons are released as radiation at the bare cavity frequency

Non-adiabatic jump of ΩR

Polaritonic vacuum

C. Ciuti, G. Bastard, IC, PRB 72, 115303 (2005)

Periodic modulation of ΩR at frequency ω

mod

● Steady-state emission of photons

● Intensity maximum on resonance with polariton frequencies

● As a function ωmod

three peaks A,B,C : 2xLP, UP+LP, 2xUP

● Emission spectrum peaked at polaritons

● Resonant-cavity-enhanced parametric luminescence

● Significant emission intensity

S. De Liberato, C. Ciuti, IC, PRL 98, 103602 �(2007)

Semiconductor devices in the ultra-strong coupling regime

G. Guenter, et al., Nature 458, 178 (2009)

How to modulate ΩR ?

● Electrons excited from valence to conduction band via interband transition in the visible range

● Coherent control of interband transition(Rabi oscillations, π-pulses...)

● Modulate effective electron density active in intersubband transition

● Switch-on and off of ultra-strong-couplingon short time scale as comparedto far-IR oscillation period

Quantum model

Isolated system Hamiltonian:

Master equation to include losses

Dissipation super-operator (weak loss approx):

Jump operators:

Dissipation baths not white(otherwise unphysical predictions)

Density of final states vj(ω), effective decay rate in → fin:

IC, S. De Liberato, D. Gerace, C. Ciuti, Back-action effects in an all-optical model of dynamical Casimir emission, in preparation

Dynamical Casimir Emission

Steady state under resonant laser g → e with Rabi frequency Ωeg

f ↔ e transition strongly coupled to cavity

Observe:● spontaneous emission on f ↔ e ● cavity emission (DCE)

For increasing Ωeg

/ωcav

:

● First threshold at Ωeg

/ωcav

= 0.5

● Stronger threshold at Ωeg

/ωcav

= 1

● Narrow and weak peak around Ωeg

/ωcav

= 1

● Strong peak around Ωeg

/ωcav

= 2

Physical origin of thresholds

Dressed state picture: g,e mixed and split by 2Ωeg

At Ωeg

/ωcav

= 0.5 :

● |g0>-|e0> exceeds in energy |g1>+|e1>● transition weakly allowed e→ f by cavity mixing

At Ωeg

/ωcav

= 1 :

● |g0>-|e0> exceeds in energy |f0>● transition fully allowed e→ f

Physical origin of peaks

Strong peak at Ωeg

/ωcav

= 1 :

● Rabi oscillations g ↔e at 2Ωeg

● periodic switch-on/off of emitter-cavity coupling● like periodic shaking of cavity mirrors: resonant DCE● resonant non-RWA coupling |g0>-|e0> ↔ |f1>

Weak peak at Ωeg

/ωcav

= 0.5 : analogous coupling via cavity

Backaction effect

Drive laser on g ↔ e transition experiences absorption by emitter

● Absorbed energy:

● Peaks in DCE give dip in absorption

● Stronger “friction” reduces absorption rate

● Easily observed with optical techniques

Conclusions

All-optical techniques to study Dynamical Casimir effect most promising:● experimental observation in circuit QED system● read-out of back-action effect on optical quantities,

much more sensitive than mechanical ones

Ultra-strong coupling systems:● vacuum state is non-trivial squeezed state with virtual photons● non-adiabatic modulation required to release them as observable radiation● possibility of sub-cycle control of intersubband far-IR transition

via interband transition driven with visible light● complete solution of simple three-level model with realistic dissipation● interesting model also from the Quantum Optics point of view

IC, S. De Liberato, D. Gerace, C. Ciuti, Back-action effects in an all-optical model of dynamical Casimir emission, in preparation