Letter Optics Letters 1 Two-dimensional electronic spectroscopy of an ultracold gas

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Letter Optics Letters 1

Two-dimensional electronic spectroscopy of an

ultracold gas

FRIEDEMANN LANDMESSER1, TOBIAS SIXT1, KATRIN DULITZ1,2,*, LUKAS BRUDER1,*,AND FRANK

STIENKEMEIER1

1Institute of Physics, University of Freiburg, Hermann-Herder-Straße 3, 79104 Freiburg, Germany

2Institut für Ionenphysik und Angewandte Physik, Universität Innsbruck, 6020 Innsbruck, Austria

*Corresponding authors: katrin.erath-dulitz@uibk.ac.at, lukas.bruder@physik.uni-freiburg.de

Compiled January 13, 2023

Femtosecond coherent multidimensional spectroscopy is

demonstrated for an ultracold gas. For this, a setup

for phase modulation spectroscopy is used to probe the

32S1/2−22P1/2,3/2transition in an 800 µK-cold sample of

7Li atoms conﬁned in a magneto-optical trap. The obser-

vation of a double quantum coherence response, a signa-

ture of interparticle interactions, paves the way for detailed

investigations of few- and many-body effects in ultracold

atomic and molecular gases using this technique. The ex-

periment combines a frequency resolution of 3 GHz with a

potential time resolution of 200 fs, which allows for high-

resolution studies of ultracold atoms and molecules both in

the frequency and in the time domain. ©

2023 Optica Publishing

Group

http://dx.doi.org/10.1364/ao.XX.XXXXXX

Ultracold atoms and molecules offer numerous exciting research

prospects in physics and chemistry, including the modelling of con-

densed matter systems [

], precision measurements of fundamental

physics [

], as well as the study of atomic and molecular interactions

and dynamics in a regime dominated by quantum effects [

]. The

presence of external ﬁelds may even be used to tune the interparticle

interaction strength [5].

The photoexcitation and photoionization of ultracold atoms pro-

vides access to research ﬁelds including ultracold Rydberg gases [

]

and ultracold plasmas [

]. Such experiments are rarely done using

femtosecond (fs) lasers, although they deliver coherent, intense laser

ﬁelds and provide access to the real-time dynamics of the excited sys-

tem. The direct observation of electronic dephasing in an ultracold

Rydberg gas, induced by an ultrashort laser pulse, provides a promi-

nent recent example for the capabilities of fs lasers in the study of

many-body effects [

]. Other recent work on the fs laser excitation

of a Bose-Einstein condensate to an ultracold microplasma has also

allowed for the monitoring of ultrafast electron cooling [9].

In general, these studies can strongly beneﬁt from spectroscopic

techniques with both high frequency and time resolution as provided by

two-dimensional electronic spectroscopy (2DES) in the fs regime [

Here, the time evolution of electronic coherences is tracked interfero-

metrically with fs pulses. The Fourier spectrum of this signal directly

relates to the absorption/emission spectrum of the sample. Further,

2DES can be combined with the phase modulation (PM) technique [

]

enabling coherent pathway selectivity of incoherent observables. The

high sensitivity of this approach is beneﬁcial for systems with low target

densities which has recently enabled 2DES studies of cold molecular

targets [

]. Moreover, most 2DES methods track the evolution

of single-quantum coherences (1QCs), that are electronic coherences

induced by one-photon transitions. The PM technique enables in addi-

tion the tracking of higher-order quantum coherences. Such

-quantum

coherence (nQC) signals provide information about multiphoton tran-

sitions and higher lying states, e.g. multi-excitonic states [

]. This

property has been used to gain access to interparticle interactions in

thermal atomic vapors, where cooperative effects are otherwise covered

by inhomogeneous broadenings [15–19].

Since ultracold atomic and molecular ensembles with their well-

deﬁned structural properties in the quantum regime are ideal testbeds

for few- and many-body effects, the combination of ultracold quan-

tum gases with coherent spectroscopy techniques, and their inherent

selectivity to weak interparticle couplings, opens up new prospects

for detailed studies of such phenomena. Here, we demonstrate the

application of 1QC and 2QC 2DES to an ensemble of ultracold atoms

in a magneto-optical trap (MOT). We choose

Li as a test system, since

the interaction of fs radiation with ultracold colliding pairs of Li atoms

in a MOT has already been studied in detail [

], so that the underlying

mechanisms are tangible.

In the experiment, the

Li atoms are cooled and trapped via the

22P3/2−22S1/2

transition (details below). The trapped atoms interact

with a sequence of four fs laser pulses resonantly driving the

32S1/2←

22P3/2

transition. The interaction with the intense fs laser pulses leads

to a multitude of linear and nonlinear signals, of which a speciﬁc subset

(described in Fig. 1(A)) is selected and detected in the experiment.

Light-matter interactions with single-atom states and collective two-

atom states (excitonic states) are possible. For a more convenient

description, we assign the states as follows:

22S1/2

state as

|2Si

22P1/2,3/2

state as

|2Pi

and

32S1/2

state as

|3Si

. The two-atom states

denoted as

|0i−|2i

correspond to both atoms in the

|2Pi

state, one

atom promoted to the

|3Si

and both atoms promoted to the

|3Si

state,

respectively.

In the 1QC 2DES measurement (Fig. 1(A)), pulses 1 and 3 induce a

coherence between the

|2Pi

and

|3Si

state, while pulses 2 and 4 project

the coherence onto the excited/ground state manifold. Accordingly, the

time evolution of the electronic coherences is probed during the time

intervals

t21

and

t43

, while the system evolves on the excited/ground

arXiv:2210.03023v2 [physics.atom-ph] 12 Jan 2023

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LetterOpticsLetters1Two-dimensionalelectronicspectroscopyofanultracoldgasFRIEDEMANNLANDMESSER1,TOBIASSIXT1,KATRINDULITZ1,2,*,LUKASBRUDER1,*,ANDFRANKSTIENKEMEIER11InstituteofPhysics,UniversityofFreiburg,Hermann-Herder-Straße3,79104Freiburg,Germany2InstitutfürIonenphysikundAngewandtePhysik,Universität...

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