Autoionizing Polaritons with the Jaynes-Cummings Model Coleman Cariker1S. Yanez-Pagans2Nathan Harkema2Eva Lindroth3Arvinder Sandhu2and Luca Argenti1 4 1Department of Physics University of Central Florida USA

2025-05-02 0 0 7.43MB 15 页 10玖币

侵权投诉

Autoionizing Polaritons with the Jaynes-Cummings Model

Coleman Cariker,1S. Yanez-Pagans,2Nathan Harkema,2Eva Lindroth,3Arvinder Sandhu,2and Luca Argenti1, 4

1Department of Physics, University of Central Florida, USA

2Department of Physics, University of Arizona, Arizona, USA

3Department of Physics, Stockholm University, Stockholm, Sweden, EU

4CREOL, University of Central Florida, USA∗

(Dated: November 7, 2024)

Intense laser pulses have the capability to couple resonances in the continuum, leading to the formation of a

split pair of autoionizing polaritons. These polaritons can exhibit extended lifetimes due to interference between

radiative and Auger decay channels. In this work, we show how an extension of the Jaynes-Cummings model

to autoionizing states quantitatively reproduces the observed phenomenology. This extended model allows us

to study how the dressing laser parameters can be tuned to control the ionization rate of the polariton multiplet.

PACS numbers: 31.15.A-, 32.30.-r, 32.80.-t, 32.80.Qk, 32.80.Zb

I. INTRODUCTION

Attosecond pump-probe spectroscopy has gained promi-

nence as a useful tool for probing and controlling ultrafast

electronic dynamics in atoms [1–14], molecules [15–22], and

condensed matter [23–25]. The electronic continuum of poly-

electronic atoms and molecules features localized transiently-

bound states, which eventually emit an electron by Auger de-

cay, a process driven by electron-electron correlation. These

states, which are essential for the control of photoelectron

emission processes [26], appear as asymmetric peaks in the

photo-absorption proﬁle of atoms and molecules, due to inter-

ference between the direct-ionization path, and the radiative

excitation of the metastable state followed by its autoioniza-

tion [27]. Quantum coherence, therefore, is an essential fea-

ture of these states, which manifests itself also in the temporal

evolution of the electronic wavefunction, when interrogated

with time resolved spectroscopies [28]. External ﬁelds can

modify the evolution of these metastable states, altering their

spectral lineshapes and lifetimes [29]. The absorption line

of bound or metastable states, when inﬂuenced by a dress-

ing laser, varies with laser intensity and the proximity of other

resonances. This variation includes phenomena such as AC

Stark shift [30], subcycle oscillations of the absorption inten-

sity [31], modiﬁcation of the lineshape asymmetry [32], and

Autler-Townes (AT) splitting [33,34]. AT splitting, in partic-

ular, has been observed in the absorption proﬁle of atoms both

above [35–38] and below [34,39,40] the ionization threshold.

In 1963, Jaynes and Cumming formulated a model for the AT

splitting of two bound states in terms of quantized radiation

states [41]. In this model, the two branches of an AT multiplet

are regarded as entangled states of atomic and light conﬁgu-

rations, known as polaritons [42–44].

Recent attosecond transient absorption measurements, cor-

roborated by theoretical calculations, have revealed AT split-

ting of the 3s−14presonance in argon, arising from its strong

radiative coupling to the 3s−13ddark state [45]. Given that

these states are subject to autoionization decay, we refer to

∗luca.argenti@ucf.edu

the AT branches as autoionizing polaritons (AIPs). Figure 1

FIG. 1. Example of an ab initio transient absorption spectrum in argon.

Here, a moderately intense dressing pulse couples the 3s−14pand 3s−13d

autoionizing states. The strong IR coupling splits the resonance into a pair

of AIPs, which are a linear combinations of the 3s−14presonance and the

3s−13d−ωIR light-induced state.

exempliﬁes this splitting in the simulated extreme ultraviolet

(XUV) attosecond transient absorption spectrum of the argon

atom. Autoionizing states (AIS), which are immersed in the

continuum, are susceptible to photoionization even by low-

energy photons like those from the infrared (IR) dressing ﬁeld.

External radiation ﬁelds, therefore, may be expected to reduce

the lifetime of these states. Contrary to expectations, in 1982,

Lambropolous and Z¨

oller posited that the Auger decay am-

plitude and the photoionization amplitude of a laser-dressed

autoionizing state might interfere destructively, thereby stabi-

lizing the state (see last paragraph in Sec. VI of [46]).

In the absence of any signiﬁcant quantum interference be-

tween radiative- and auto-ionization amplitudes, the AIPs

formed by resonant bright and dark states should have iden-

tical widths. However, the measurements presented in [45]

show that the widths of the two polaritons do differ, with one

polariton being narrower than the original bright state, which

is evidence of the coherent stabilization process predicted by

Lambropoulos and Z¨

oller. The interference between radiative

arXiv:2210.01712v3 [physics.atom-ph] 6 Nov 2024

and autoionization amplitudes enhancement in the AIP decay

can be controlled via the laser parameters. AIPs, therefore,

qualitatively differ from both bound-state polaritons, which

do not have access to Auger decay channels, and overlapping

autoionizing states, where radiation does not play any role.

In this study, we reproduce some of the main features

of overlapping autoionizing polaritons in the argon atom by

means of ab initio simulations. To explain the proﬁles ob-

served in the simulations, we use Fano’s approach to extend

the Jaynes-Cummings (JC) to autoionizing states. Our model

is capable of describing the optical excitation, from an initial

ground state |g⟩, of multiple autoionizing states coupled to

each other by an external infrared driving ﬁeld, and their sub-

sequent decay to the continuum. It quantiﬁes the interference

between radiative and nonradiative decay pathways, illustrat-

ing how a laser can stabilize an autoionizing state, and it pro-

vides a functional form for the lineshape due to overlapping

polaritons in transient absorption spectra, which was essential

to extract the polariton parameters from the experiment [45].

This contribution is a stepping stone for understanding co-

herent control of polaritonic states in matter, a key aspect of

emerging technologies in quantum sensing [47], photon trap-

ping, and quantum information processing [48].

This paper is organized as follows. In Section II, we de-

scribe the ab initio many-body calculations of argon’s res-

onant attosecond transient-absorption using the NEWSTOCK

suite [45,49], demonstrating convergence of the results with

a limited essential-state space. Section III introduces an ele-

mentary version of the extended JC model, applicable to two

non-overlapping resonances when the direct ionization am-

plitude from the ground state to the continuum is negligible.

This simpliﬁed model is already capable of demonstrating the

mechanism of destructive and constructive interference re-

sponsible for the stabilization and destabilization of the au-

toionizing polaritons observed in the ab initio simulations and

in the experiment. Section IV describes a more general ex-

tended JC model suited to describe multiple laser-coupled au-

toionizing states alongside a non-negligible direct ionization

amplitude from the ground state to the continuum. This model

is essential to derive the functional form for the proﬁle of po-

laritonic multiplets, which is needed to extract the position

and width of these states from experimental spectra. In sec-

tion Vwe provide our conclusions.

II. AB INITIO CALCULATIONS

In this section we present the results of ab initio simulations

of the transient absorption spectrum of argon, focusing on the

case where the 3s−14presonance is excited by a weak XUV

pump pulse, with a duration of few femtosecond, while being

dressed by a moderately strong IR probe pulse. Depending on

its central frequency, the IR pulse may bring in resonance the

3s−14pbright state with other dark or bright resonances by

means of one-photon or two-photon transitions, thus causing

the resonance peak to split into a pair of AIPs.

For our study, we assume that both the pump and probe

pulses are linearly polarized along the same quantization axis.

To reproduce the observables measured in a realistic experi-

ment, we compute the transient absorption spectrum both as

a function of the pump-probe delay (keeping the IR intensity

and frequency constant) and as a function of the IR frequency

(at a ﬁxed time delay).

In our ab initio atomic structure calculations, we employ

the NEWSTOCK suite of atomic codes, which expresses the

wave function for the neutral system a time-dependent ex-

tended close-coupling (CC) expansion

Ψ(x;t) = X

Γ"X

αAΦΓ

α(¯

x; ˆrNe, ζNe)φΓ

α(rNe;t) +

+⟨x|KΓ⟩cΓ(t)#,

(1)

where the vectors x= (x1, x2, . . . , xNe)and ¯

(x1, x2, . . . , xNe−1)contain the spatial and spin coordinates

for the electrons in the neutral atom and in the ion, respec-

tively, with xi= (⃗ri, ζi), and A=1

Ne!PP∈SNesgn(P)P

is the antisymmetrizer. The index αidentiﬁes a partial-wave

channel (PWC), i.e., a speciﬁc ionic state coupled to a photo-

electron with deﬁnite orbital angular momentum to give rise

to an atomic state with speciﬁed parity, Π, orbital angular mo-

mentum, L, spin, S, and their respective projections, Mand

Σ, indicated collectively by the symbol Γ = (Π, L, S, M, Σ),

ΦΓ

α(¯

x; ˆrNe, ζNe) = X

MamX

Σaσ

CLM

LaMa,ℓmCSΣ

SaΣa,1

2σ×

×ϕa(¯

x)Yℓm(ˆrNe)2χσ(ζNe),

(2)

where Cℓ12 ,m12

ℓ1m1,ℓ2m2are Clebsch-Gordan coefﬁcients, ϕa(¯

x)is

the state of the ion in channel α,Yℓm(ˆr)are spherical har-

monics, 2χσ(ζ) = ⟨ζ|σ⟩=δσζ , with σ, ζ =±1

2, are

spin eigenfunctions, whereas φΓ

α(r;t)in (1), is the photo-

electron radial function, which can depend on time. Fi-

nally the row vector |KΓ⟩= (|KΓ

1⟩,|KΓ

2⟩, . . .)speciﬁes a

set of conﬁguration-state functions (CSFs), complementary

to the PWC functions, called localized channel (LC), where

KΓ

iis a given atomic CSF, e.g., 1s22s22p63s23p54s(1Po),

1s22s22p63s23p4(3Pe)4s(2Pe)4p(1Po), etc. The ionic

functions ϕa(¯

x) = ⟨¯

x|ϕa⟩are themselves expressed in terms

of a set of ionic CSFs, |¯

K⟩,

|ϕa⟩=X

K|¯

KΓa⟩CΓa

K,a.(3)

In this work, the ionic CSFs arise from the follow-

ing shell occupations (for brevity, the inactive neon

1s22s22p6core is not speciﬁed): 3s23p5,3s23p43d,

3s23p44s,3s23p44p,3s23p33d2,3s23p33d4s,3s23p33d4p,

3s23p34s4p,3s23p34p2,3s23p23d3,3s23p23d24s,3s3p6,

3s3p53d,3s3p54p,3s3p43d2,3s3p43d4s,3s3p43d4p, and

3p53d2, which give rise to 25 2Se, 40 2Po, 51 2Pe, and 65

2Deionic CSFs. The orbitals and the ionic states are opti-

mized using the Multi-conﬁguration Hartree-Fock (MCHF),

implemented in the ATSP2Katomic-structure package [50],

by minimizing the weighted average of the energy of the ﬁrst

2Seand the ﬁrst 2Postates of the ion, which have dominant

conﬁguration [Ar]3s−1and [Ar]3p−1, respectively. To con-

struct the PWCs used in 1, we couple the ﬁrst two MCHF

ions in each of the 2Po,2Se,2De, and 2Peion symme-

tries, to photoelectrons with orbital angular momentum up

to ℓmax = 4, resulting in 6, 12, 4, 14, 12, and 10 PWCs in

the neutral-atom symmetries 1Se,1Po,1Pe,1De,1Fo, and

1Ge, respectively. The radial functions for the PWC photo-

electrons are selected within the orthogonal complement to

the ionic active orbitals of a space of radial B-splines [49,51]

with order 7, spanning the interval r∈[0 : RBOX]a.u., with

RBOX = 500 a.u. and an asymptotic spacing of 0.4 a.u. be-

tween consecutive nodes. The LC in (1) consists of all the

conﬁgurations formed by adding an electron in any of the ac-

tive ionic orbitals 3s, 3p, 3d, 4s, 4pto any of the ionic CSFs.

The size of the LCs in the various symmetries is: 193 for 1Se,

435 for 1Po, 314 for 1Pe, 509 for 1De, 449 for 1Fo, and 339

for 1Ge.

The initial ground state of the system, |g⟩, is obtained by

diagonalizing the ﬁeld-free electrostatic Hamiltonian ˆ

H0in

the close-coupling basis. Formally, the subsequent evolution

of the system under the inﬂuence of the external sequence of

pump and probe pulses is determined by solving the time-

dependent Schr¨

odinger equation (TDSE), within the dipole

approximation, in velocity gauge [52],

iℏ∂t|Ψ(t)⟩=ˆ

H0+1

c⃗

A(t)·ˆ

⃗

P|Ψ(t)⟩,|Ψ(ti)⟩=|g⟩,

(4)

where ˆ

⃗

P=PNe

i=1 ˆ

⃗piis the total electron linear momentum

and ⃗

A(t) = ˆz A(t)is the vector potential of the external ﬁeld.

Gauss units [53] and atomic units (ℏ= 1,me= 1,qe=

−1) are used throughout the paper unless speciﬁed otherwise.

The absorption spectrum, or optical density (OD), in the XUV

region is ﬁnally determined from the Fourier Transform of the

dipole expectation value along the ﬁeld polarization, ˜

P(ω) =

Reiωt P(t)dt, where P(t) = ⟨Ψ(t)|ˆ

Pz|Ψ(t)⟩dt, using the

formula

σ(ω) = −4π

ωIm "˜

P(ω)

A(ω)#,(5)

In practice, the XUV components OD are largely insen-

sitive to the portion of the wave function far from the nu-

cleus. Furthermore, propagation in a ﬁnite box would even-

tually lead to unphysical reﬂections at the box boundaries

which would manifest themselves as spurious noise in the

spectrum, as the reﬂected wave packet returns to the inter-

action region. This circumstance indicates both that artiﬁcial

reﬂections must be prevented and that the conﬁguration space

could be signiﬁcantly reduced. We achieve both goals by in-

troducing in the ﬁeld-free Hamiltonian a complex absorption

potential VCAP, deﬁned as

VCAP =−iΓCAP

i=1

θ(ˆri−RCAP)(ˆri−RCAP)2,(6)

where ΓCAP and RCAP are real positive constants, and θ(x) =

−∞ dx′δ(x′)is the Heaviside step function. In this calcu-

FIG. 2. Depiction of states retained from close-coupling calculations

for the essential states basis, with symmetry 1Se(crosses, magenta

online), 1Po(full square, green online), 1De(full circles, cyan on-

line), and 1Fo(full triangles, orange online).

lation, RCAP =RBOX −50 a.u.= 450 a.u., and ΓCAP =

8×10−4. The CAP estinguishes the wavefunction before it

reaches the boundary of the quantization box, without causing

itself any appreciable reﬂections.

The matrix representative in the CC basis |χ⟩=

(|χ1⟩,|χ2⟩, . . .)of the complex symmetric ﬁeld-free Hamil-

tonian with the CAP, H0+VCAP =⟨χ|ˆ

H0+ˆ

VCAP|χ⟩, is

diagonalized,

H0+VCAP =UR˜

E U†

L,˜

Eij =˜

Eiδij ,(7)

where ˜

Ei=¯

Ei−iΓi/2are complex eigenvalues with nega-

tive imaginary parts, ¯

Ei,Γi∈R,Γi≥0. The matrices UR/L

are collections of right and left eigenvectors of the Hamil-

tonian, normalized such that U†

LUR=1. The CAP effec-

tively enforces outgoing boundary conditions on the autoion-

izing states of the system, which in this calculation appear

as isolated eigenvectors of the complex Hamiltonian. There-

fore, for ri< RCAP, the autoionizing states obtained with this

procedure are Siegert states of the atom [54,55]. In the fol-

lowing, therefore, we will refer to the basis of the UReigen-

states of the complex Hamiltonian as Siegert-state (SS) ba-

sis. Figure 2shows a section of the complex spectrum of the

quenched Hamiltonian in 1Se,1Po,1De, and 1Fosymme-

try. In the ﬁgure, we can clearly distinguish three main types

of eigenvalues: bound states, with zero imaginary part, lo-

cated below the ﬁrst ionization threshold; discretized contin-

uum states, branching off from the real axis at each channel’s

threshold Eth with increasingly negative imaginary parts; and

autoionizing states, which correspond to isolated poles near

the real axis, largely insensitive to the speciﬁc value of ΓCAP

(as soon as it is large enough), and which here form Ryd-

berg series converging to the ion shake-up thresholds. When

the TDSE is propagated in the SS basis, we observed that the

basis can be reduced to as little as 1% of its full size, retain-

ing only the states in the spectral region of interest — e.g.,

those delimited by the red frame in Fig. 2— without affect-

ing the quality of the simulated absorption spectrum. This

remarkable ﬁnding reﬂects the circumstance that the transient

absorption spectrum primarily probes the inner region of the

wave function. We refer to this smaller set of state vectors as

essential-state (ES) basis.

文档加载中……请稍候！
如果长时间未打开，您也可以点击刷新试试。

下载文档到电脑，查找使用更方便

10 玖币 0人已下载

立即下载

摘要：

AutoionizingPolaritonswiththeJaynes-CummingsModelColemanCariker,1S.Yanez-Pagans,2NathanHarkema,2EvaLindroth,3ArvinderSandhu,2andLucaArgenti1,41DepartmentofPhysics,UniversityofCentralFlorida,USA2DepartmentofPhysics,UniversityofArizona,Arizona,USA3DepartmentofPhysics,StockholmUniversity,Stockholm,Swed...

展开>> 收起<<

Autoionizing Polaritons with the Jaynes-Cummings Model Coleman Cariker1S. Yanez-Pagans2Nathan Harkema2Eva Lindroth3Arvinder Sandhu2and Luca Argenti1 4 1Department of Physics University of Central Florida USA.pdf

共15页,预览3页

还剩页未读，继续阅读

声明：本站为文档C2C交易模式，即用户上传的文档直接被用户下载，本站只是中间服务平台，本站所有文档下载所得的收益归上传人(含作者)所有。玖贝云文库仅提供信息存储空间，仅对用户上传内容的表现方式做保护处理，对上载内容本身不做任何修改或编辑。若文档所含内容侵犯了您的版权或隐私，请立即通知玖贝云文库，我们立即给予删除！

Autoionizing Polaritons with the Jaynes-Cummings Model Coleman Cariker1S. Yanez-Pagans2Nathan Harkema2Eva Lindroth3Arvinder Sandhu2and Luca Argenti1 4 1Department of Physics University of Central Florida USA

相关推荐

开通VIP享超值会员特权

作者详情

相关内容

热门标签

举报选择: