Experimental observation of fractional echoes

Abstract

We report the observation of fractional echoes in a double-pulse excited nonlinear syst em . Unlike standard echoes which appear p eriodically at delays which are integer multiple of the delay between the two exciting pulses, the fractional echoes appear at rational fractions of this delay. We discuss the mechanism leading to this phenomenon, and provide the first experimental demonstration of fractional echoes by measuring third harmonic generation in a thermal gas of C02 molecules excited by a pair of femtosecond laser pulses . 37.10.Vz, 42. 50. Md Many nonlinear syst ems display the phenomenon of echoes, which is a series of delayed impulsive responses after a pair of short external pulses . These echoes typ-· icany show themselves at times T rv T , 2T, 3T, etc. after the end of the excitation, where T is the delay between the stimulating pulses . Echoes are common in many ar-· eas of physics, including NMR [1] , plasma physics [2--4], nonlinear optics [5], cavity quantum electrodynam-· ics [6 , 7], and cold atoms physics [8][9][10][11] . Echoes were predict ed to occur in proton storage rings [12 , 13], and were observed in high energy hadron b eam experiments [14,15] . Echo-enabled generation of short-wavelength ra-· diation in free-electron lasers [16][17][18] was demonstrat ed (for a recent review, see [19]) .Recently we reported the exist ence of orienta-· tion/ alignment echoes in an ensemble of free classi-· cal rotors stimulat ed by an external impulsive force [20] . We attributed t he echo formation to the kick-· induced filamentation of the rotational ph ase space, and demonstrated the effect experimentally in a gas of C0 2 molecules excited by a pair of femtosecond laser pulses. The time-dependent mean molecular alignment (defined as (cos 2 (B) )(t) , where e is the angle between t he molec-· ular axis and laser polarization) was measured via the laser-induced birefringence signaL The excited syst em exhibited a regular sequence of echo pulses at delays T = T , 2T, 3T, . . . . In addition, our theoretical analysis and numerical simulations [20] also predict ed unusual ad-· ditional recurrences (fractional echoes) at T = (p j q)T, where p and q are mutuany prime numbers. These frac-· tional echoes, however cannot be seen in the alignment signal -t hey require measurement of higher order mo-· ments of the molecular angular distribution.Here we present the first observation of the phe-· nomenon of fractional echoes measured via third-· harmonic generation (THG) in a gas of C0 2 molecules at room t emperature and pressure of 80 mbar. In what follows we introduce the mechanism of the fractional echoes by using a simple 2D classical model, and then describe our experiments in which t he phenomenon of fractional echoes was observed . We also compare the experimental result s to the fun three-dimensional classical and quantum simulations of the echo formation .For a nonresonant laser field interacting with a symmetric linear molecule, such as N 2 , 0 2 or C0 2 , the angular-dependent interaction potent...

Orientation and Alignment Echoes

“…Our qualitative analysis reveals the echo m echanism and predicts its dependence on param eters of the stimulating kicks. A full analytical theory o f these echoes in 2D and 3D thermal ensem bles o f classical rotors, and its generalization to the quantum case will be published elsewhere [21]. Here, we discuss the physics behind the predicted echo effect and dem onstrate it experim entally in a collection o f C 0 2 molecules stim ulated by a pair of femtosecond laser pulses.…”

All-optical measurement of high-order fractional molecular echoes by high-order harmonic generation

“…In order to visualize higherorder fractional molecular echoes, one can increase the delay of the pump pulses. However, for CO 2 , the interplay of quantum revival and echo phenomenon will show up when the delay of the pump pulses is further increased [19,20]. Alternatively, we adopt the N 2 O as the sample gas, which has a similar revival period (T rev =39.9 ps) as CO 2 .…”

“…The formation of these echoes can be theoretically explained as a consequence of the kickinduced filamentation of the rotational phase space [18][19][20]. In addition to the echoes at τ = N T (also called the full echoes), G. Karras et al also predicted some additional remarkable recurrences (which are referred to fractional echoes) at times that are rational fractions of the delay between the pump pulses [18,19]. To observe the fractional echoes, it requires measurement of higher order moments of the molecular angular distribution, which * Electronic address: *Corresponding author: helxḣ ust@mail.hust.edu.cn,pengfeilan@mail.hust.edu.cn however cannot be achieved in the birefringence measurement.…”

“…To observe the fractional echoes, it requires measurement of higher order moments of the molecular angular distribution, which * Electronic address: *Corresponding author: helxḣ ust@mail.hust.edu.cn,pengfeilan@mail.hust.edu.cn however cannot be achieved in the birefringence measurement. Very recently, the lowest-order (1/2) fractional echo in molecules was optically detected by measuring the third harmonic of the probe pulse [19]. While Lin et al have also demonstrated the measurement of fractional molecular echoes (up to 1/3) with Coulomb explosion imaging (CEI) method [20], a purely optical technique to probe high-order fractional molecular echoes is still lacking.…”

Spatiotemporal rotational dynamics of laser-driven molecules

“…Such wave packets provide a unique opportunity for exploring fundamental quantum phenomena, i.e., quantum revivals, [29][30][31][32][33] Anderson localization, 34 and Bloch oscillations. 35 More recently, a new classical phenomenon of molecular alignment echo [36][37][38] was reported, where much like other echoes, following excitation by a pair of time-delayed short laser pulses, a series of impulsive responses (echoes) appear, with a period equal to the time delay between the two initial pulses.…”