Two photon absorption and coherent control with broadband down-converted light

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by  Barak Dayan

Two photon absorption and coherent control with broadband down-converted light
Barak Dayan, Avi Pe’er, Asher A. Friesem, and Yaron Silberberg
∗ † ‡
Department of Physics of Complex Systems,
Weizmann Institute of Science,
Rehovot 76100, Israel
We experimentally demonstrate two-photon absorption (TPA) with broadband down-converted
light(squeezedvacuum). Althoughincoherentandexhibitingthestatisticsofathermalnoise,broad-
banddown-convertedlightcan induceTPAwiththesamesharptemporalbehaviorasfemtosecond
pulses, while exhibiting the high spectral resolution of the narrowband pump laser. Using pulse-
shaping methods, we coherently control TPA in Rubidium, demonstrating spectral and temporal
resolutions that are 3-5 orders of magnitude below theactual bandwidth and temporal duration of
the light itself. Such properties can be exploited in various applications such as spread-spectrum
4 optical communications, tomography and nonlinear microscopy.
0
0
PACSnumbers: 32.80.Qk,42.50.Ct,42.50.Dv,42.65.Ky,42.65.Lm,42.65.Re
2

n
a In two-photon absorption (TPA), two photons whose with a spectral bandwidth that exceeds a certain limit
J sum energy equals that of an atomic transition, must can induce TPA just like transform-limited pulses with

5 arrive at the atom together. The two, seemingly con- the same bandwidth. Consequently, the interaction
1 tradicting, demands of a narrow temporal and a narrow exhibits a sharp, pulse-like temporal behavior, and can

spectral behavior of the inducing light are typically be coherently controlled by pulse-shaping techniques,
1
maximized by transform-limited pulses, which exhibit eventhoughthedown-convertedlightisneithercoherent
v
8 the highest peak intensity possible for a given spectral nor pulsed. This effect occurs as long as the transition
8 bandwidth. Nonetheless, it was shown [1, 2, 3, 4] that energy lies within the spectrum of the pump laser that
0 pulses can be shaped in a way that will stretch them generated the light; thus, the spectral selectivity of
1
temporally yet will not affect the transition probability, the interaction is dictated by the narrowband pump
0
and even increase it in certain cases. Other experiments laser and not by the orders of magnitude wider band-
4
0 have exploited coherent control [5, 6, 7, 8] to increase width of down-converted light itself. We demonstrate
/ the spectral selectivity of nonlinear interactions induced these principles experimentally by inducing and co-
h
by ultrashort pulses [9, 10, 11]; however, the spectral herently controlling TPA in atomic Rubidium with
p
- resolution demonstrated by these methods remains down-converted light, and obtaining results that are
t
n considerably inferior to that obtained by narrowband, practically identical to those obtained with coherent
a continuous lasers. Few experiments [12, 13] have per- ultrashort pulses.
u
formedTPA with coherent,narrowbanddown-converted
q
light, demonstrating nonclassical features which appear The underlying principle that enables coherent TPA
:
v at very low powers [14, 15, 16], and result from the time withbroadbanddown-convertedlightisbasedonthefact
i
X and energy correlations (entanglement) between the thatthequantuminterferencethatgovernsTPAinvolves
down-convertedphoton-pairs[17, 18, 19]. Athigh power pairsofelectromagneticmodes. Sincetheexcitationofan
r
a levels(as those discussedinthis work)these correlations atomiclevelwithfrequencyΩmaybeinducedbyanytwo
vanish, yet similarly nonclassical phase and amplitude photons with frequencies ω and Ω ω , regardlessof the
−
correlations [20, 21] appear between the signal and idler exact value of ω, the final population p is proportional
f
beams. Unlike the time and energy correlations at low to [2]:
powers, these phase and amplitude correlations cannot
bedescribedintheusualformofsecond-ordercoherence.
2
At sufficiently high powers, which greatly exceed the p E(ω)E(Ω ω)dω , (1)
single-photons regime, broadband down-converted light f ∝(cid:12)(cid:12)Z − (cid:12)(cid:12)
(cid:12) (cid:12)
that is pumped by a narrowband laser is inherently (cid:12) (cid:12)
where E(ω) is the spectral amplitude of the light. As
incoherent, and exhibits the properties of a broadband
is obvious from Eq. (1), it does not matter whether
thermal noise [17, 22]; consequently, it is not expected
E(ω)hasadefinedphaseforeveryω,butratherwhether
to be effective at inducing TPA. Nevertheless, it was
the product E(ω)E(Ω ω) has a defined phase for ev-
shown that at the appropriate conditions, the quantum −
ery ω. Despite the incoherence of each of the down-
correlations within the down-converted spectrum can
converted signal and idler beams, they exhibit exactly
give rise to efficient sum-frequency generation [23, 24].
this mutually-coherent phase behavior at frequency-
pairs,due to the inherentphase andamplitude quantum
Inthisworkweshowthatdown-convertedlightbeams correlations within the down-converted spectrum [20]:
2
a 4D5/2,1/2 b
Computer
5P1/2 Pump
Idler
~ 1270 nm Signal SLM Digital
oscilloscope
Pump
780 nm 516.65 nm
Idler PMT
Signal Delay line
~ 870 nm
Rb cell
5S1/2
FIG. 1: Experimental setup for TPA with broadband down-converted light. (a) Atomic energy levels of Rb, showing the
two-photon transition induced by the broadband signal and idler beams between the 5S and the 4D levels, and the resulting
decay through the 5P levels. (b) The experimental layout. 3 ns pulses at 516.65 nm were used to pump a 14 mm long BBO
crystal that was located inside a low-finesse resonator. The relative angles between the crystal axis, the pump laser and the
resonator were chosen to obtain broadband phase matching for non-collinear type-I down-conversion, with the signal beam
propagating in thedirection of theresonator, andtheidler beam divergingfrom it at an angleof 11◦. Unlikethesignal beam,
whosedirectionofpropagationwassetbytheresonator,theidlerbeamhadawavelength-dependentangularspread,duetothe
phase matching conditions in the crystal. Therefore, it was directed through an imaging system that included a transmission
grating which compensated for this spread. The signal beam was directed through a pulse shaper and a computer-controlled
delay line with 0.1 µ resolution, and then combined with the idler beam by a dichroic mirror. The pulse shaper separates the
spectral components of the beam and utilizes a computer-controlled spatial light modulator (SLM) to introduce the desired
spectral phase filter to the light, before recombining the spectral components back to a single beam. The combined signal
and idler beams then entered the Rb cell. A photo-multiplier tube (PMT) and a digital oscilloscope were used to perform a
triggered measurement of theTPA-induced fluorescence.
bandwidththatmaybe5-7ordersofmagnitudebroader.
√1ω Es(ω) ≈ √ω1p−ω Ei∗(ωp−ω), (2) [25A], cwohmicphletteakqeusainnttuoma-cmcoeuchnatntihcaelsapneacltyratilcbcaanlcduwlaidttiohns
where ωp is the pump frequency, and Es(ω), Ei(ω) of the pump laser and of the atomic level, shows that
denotethespectralamplitudesofthesignalandtheidler the TPA signal is composed of two parts, which may be
beams, respectively. In the case of TPA induced by the referred to as the ’coherent TPA’ and the ’incoherent
combined signal and idler beams from the same source, TPA’. The coherent TPA results from the summation
these correlations have a drastic effect when the pump of conjugated spectral components, and indeed can be
frequency is equal to the total transition frequency. coherentlycontrolled. The incoherentTPA,however,re-
Combining Equations (1) and (2), letting ωp = Ω, sults from the summation of all other random spectral
reveals that the random phase of Es(ω) is always com- combinations and is a direct result of the incoherence
pensatedby the opposite phaseofEi(ωp ω). Thus,the of the down-converted light; therefore it is unaffected
−
integrand in Eq. (1) has a constant phase, leading to a by spectral-phase manipulations and may be regarded
full constructiveinterference ofall the spectral combina- as a background noise, which limits the equivalence of
tions, exactly as if the interaction was induced by a pair the down-converted light to a coherent pulse. The ratio
of transform-limited pulses with the same spectra as the between the coherent term Ic and the incoherent term
signal and idler beams. Moreover,this TPA process will Iic can be approximated by :
besensitivetominutedelaysbetweenthesignalandidler
beams, to dispersion and even to pulse shaping, exactly Ic B n2+ 21πn , (3)
as if it was induced by a pair of ultrashort pulses. Since Iic ≈ (γ +γ ) n2
p f
this constructive interference occurs only when the final
where n is the spectral averageof the mean photon flux,
stateenergyfallswithin the spectrumofthe pump laser,
and B,γ ,γ are the bandwidths of the down-converted
the spectral resolution of the TPA process will be equal p f
light, the pump laser and the final state, respectively.
to the spectral bandwidth of the pump laser, regardless
This expression reveals the importance of using spec-
of the actual bandwidth of the down-converted light
trally broad down-converted light. The coherent term
itself. Note that in the case of a continuous pump
becomes dominant only when the down-converted
laser, this implies a possible spectral resolution of a
bandwidth exceeds both the pump bandwidth and the
few MHz or even less, which is phenomenally high for
an interaction that is induced by light with a spectral final level width: B > (γp+γf)(n2+n221πn). Equation (3)
3
shows that the coherent term exhibits a linear intensity
1 (a) 1 (b)
dependence at low powers, as was previously shown
[14, 15] and experimentally observed [12]. 0.8 0.8
u.] u.]
Our experimental layout is described in Fig. 1. The a. 0.6 a. 0.6
pumplaser(Spectra-PhysicsMOPO-SLlaser)wastuned A [ A [
P P
to emit 3 ns pulses with a bandwidth of 0.04 nm T 0.4 T 0.4
around 516.65 nm, which corresponds to the 5S 4D
− 0.2 0.2
transition in Rb (Fig. 1a). These pulses pumped a
BBO crystal that was located inside a low-finesse res- 0 0
-200 -100 0 100 200 516.4 516.6 516.8 517.0
onator, with the phase-matching conditions chosen to
Signal-idler relative delay [fs] Pump wavelength [nm]
obtain broadband ( 100 nm each), non-collinear sig-
∼
nal and idler beams. The signal beam was directed
through a computer-controlled pulse-shaper, which is FIG. 2: Experimental TPA with broadband down-converted
normally used to temporally shape femtosecond pulses light, as a function of the signal-idler delay and the pump
and performs as a spectral-phase filter [26]. From the wavelength. The graphs clearly show a coherent TPA signal
pulse-shaper the signal beam continued to a computer- that is narrow both temporally and spectrally, superimposed
on an incoherent background signal, which is insensitive to
controlled delay line, and then was combined with the
bothpumpwavelengthandsignal-idlerrelativedelay. Inthis
idler beam by a dichroic mirror. The combined beams
experimentthepulseshaperwasusedonlytocompensatefor
entered the Rb cell, and the induced TPA was measured
thedispersioninoursystem. (a)Calculated(line)andexper-
through the resulting fluorescence at 780 nm. Our anal- imental TPA with off-resonance (squares) and on-resonance
ysis predicts that the down-converted beams, each 3 ns (circles) pump, as a function of the signal-idler delay. (b)
long with a peak power of about 1 MW and a spectral Experimental TPA at zero signal-idler delay (circles), and at
bandwidthofabout100nm,shouldinduceTPAwiththe 100fssignal-idlerdelay(squares),asafunctionofthepump
center wavelength, together with a typical spectrum of the
same efficiency and temporal resolution as 23 fs pulses
pump (line). The coherent TPA signal appears only when
with a peak power of about 150 GW, while exhibiting a
the pump is on-resonance with the 5S−4D transition, and
spectral resolution of 0.04 nm.
exhibitsasharpdependenceonthesignal-idlerdelay,exactly
as if theinteraction was inducedbya pairof coherent, 23 fs
Toverifythese predictionsexperimentally,wescanned pulses with thesame spectra as thesignal and idler beams.
both the pump wavelength and the relative delay be-
tween the signal and idler beams. Fig. 2 shows the TPA spectral width of the coherent TPA is dictated by the
signalversusthesignal-idlerrelativedelayandthepump- bandwidth of the pump laser (0.04 nm) and the width
wavelength. As is evident, for off-resonance pump or for of the (power-broadened) 4D level ( 0.08 nm). This
∼
largesignal-idlerdelays,onlylowefficiencyTPAsignalis spectralresolutionis 2000timesnarrowerthanthetotal
observed,whichis insensitiveto either pumpwavelength bandwidth of the down-converted light.
or signal-idlerdelay. This signalcorrespondsto the clas-
sical,incoherentTPAbackgroundsignal. However,when
Finally, we demonstrated coherent quantum control
the pump wavelength was set to the 5S 4D transition
− over the coherent TPA process, in a similar way to
resonance, an additional, high efficiency, TPA signal ap-
coherent control of TPA with ultrashort pulses [1]. For
peared. The sharp response of this coherent TPA signal
that we used the pulse shaper to apply a square-wave
toafewfemtosecondsdelaybetweenthebeamsispracti-
phase filter on the signal spectrum (Fig. 3a). With
cally identical to the case of TPA induced by two coher-
ultrashortpulses this has the effect of splitting the pulse
ent, 23fs pulses. This temporalresolutionis 5 ordersof
temporally to a train of several smaller pulses. Fig. 3b
magnitudebetterthantheactual3nstemporalduration
showsprecisely this behaviorofthe coherentTPAsignal
of the down-convertedlight.
asafunctionofthesignal-idlerdelay. Fig. 3cdepictsthe
Since the peak power of the equivalent transform-
experimental and theoretical TPA signal at zero delay
limited pulses is extremely high (150 GW), the signal
as a function of the magnitude of the square wave phase
and idler beams had to be expanded and attenuated
filter. The results, which are identical to those obtained
in order to avoid complete saturation of the transition.
incoherentcontrolexperimentswithfemtosecondpulses,
Unfortunately,wecouldnotattenuatethebeamsenough
showthecyclictransitionbetweencompleteconstructive
to avoid saturation completely, due to high levels of
and destructive quantum interference of the different
noise in our system. As a result, our measurements
spectral sections, and demonstrate the ability to fully
had to be performed in a partially saturated regime,
control the coherent TPA process.
where the measured intensity dependence of the TPA
process was less than quadratic, and the 4D level
was power-broadened. Thus, the observed 0.12 nm Broadband down-conversion of a narrowband pump
4
2p
(a) 1 (b) 1 (c)
m
er u
al phase filt p ower spectr PA [a.u.] 00..68 PA [a.u.] 00..68
ectr al p T 0.4 T 0.4
p n
S Sig 0.2 0.2
0 0 0
800 850 900 950 -400 -200 0 200 400 0 p 2p 3p 4p 5p 6p
Wavelength [nm] Signal-idler relative delay [fs] Phase filter magnitude [rad]
FIG. 3: Experimental coherent quantum control of TPA with down-converted light. (a) The square-wave spectral phase filter
applied on the signal beam by the pulse-shaper, together with a typical power spectrum of the signal. (b) Experimental
(circles) and calculated (line) TPA signal as a function of the signal-idler delay, with a spectral square-wave phase filter with
magnitude π applied to the signal beam. The splitting of the central peak confirms that the coherent TPA behaves exactly
as if it was induced by a pair of transform-limited pulses, with one of them temporally shaped by the applied phase filter.
(c) Experimental (circles) and calculated (line) TPA signal as a function of the magnitude of the square wave spectral phase
filter. ThegraphshowstheperiodicannihilationofthecoherentTPAatmagnitudesofπ,3π,5π,whereacompletedestructive
quantuminterference occurs(’dark pulse’),and thecomplete reconstruction of theTPA signal at amplitudesof 2π,4π,6π etc,
demonstrating complete quantumcontrol over thecoherent TPA process.
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