Observation of spatially localized atomic electron wave packets

Abstract

We have excited and detected an atomic electron wave packet that is localized in the polar and azimuthal angles. The wave packet is formed through the coherent superposition of Rydberg states of atomic sodium. The superposition is achieved by short-pulse optical excitation of the atom in the presence of a strong rf field. The wave packet is detected by dc field ionization. The behavior of this wave packet in a strong dc field is much different from that of an eigenstate. This behavior agrees well with a simple classical model. PACS numbers: 32.90.+a, 31.50,+w, Several recent papers 1 " 5 have discussed the possibility of forming a localized wave packet through the coherent superposition of atomic Rydberg states. The study of atomic coherent states began 6 shortly after the development of quantum mechanics and the theoretical treatment of these states has been extensive. 6 " 10 The fundamental concern of these studies is to understand the transition between classical and quantum physics. Recently, the interest in these states has increased because of the development of short-pulse lasers. The large coherent bandwidth of these pulses makes it likely that the result of this field acting upon an atom is best described in terms of atomic coherent states. In our previous paper 4 we proposed the excitation of a Rydberg atomic wave packet localized in two of the spherical coordinates, the polar and azimuthal angles. Here we report the observation of such a wave packet and examine its behavior in a strong dc field. This behavior agrees well with a simple classical model.The wave packet is formed in the high-angularmomentum Rydberg states of atomic sodium. The advantages of the use of such states are several, as has been demonstrated by the recent experiment on inhibited spontaneous emission. 11 The chief advantage, for this experiment, is the possibility of our obtaining a nearly uniform energy spacing between the excited eigenstates. This reduces the rate at which the wave packet disperses. Another feature is the exceedingly large electric dipole matrix elements that exist between neighboring states: A modest rf field is sufficient to dress strongly states with the same principal quantum number. This dressing plays a critical role in the excitation of the wave packet.The excitation of the angularly localized wave packet is achieved through the optical excitation of Rydberg states that are being strongly dressed by an rf field. A circularly polarized optical field is tuned to the twophoton resonance between the ground state and the ^=•50 (principal quantum number) manifold of states. This manifold of states is being strongly dressed by a circularly polarized rf field, tuned near the thirty-photon resonance between the 50d state and the / a =32 state. This high-angular-momentum state and several of its neighbors are strongly mixed with the 50d state. All of these rf-dressed states lie within the coherent bandwidth of the optical pulse and can be excited by it. Following an adiabatic turnoff of the rf field, the population ...

Non-dispersive wave packets in periodically driven quantum systems

“…This implies that the temporal dynamics is built from exactly the same frequencies; thus, the 3D dynamics is essentially the same as the 1D dynamics. 5 Indeed, collapses and revivals of the wave-packet were also observed, under various experimental conditions, in the laboratory [5,11,25,26]. Fig.…”

“…There have been several experimental realizations of electronic wave-packets in atoms [4,5,11,25,27,28], either along the pure radial coordinate or even along angular coordinates too. However, all these wave-packets dispersed rather quickly.…”

“…The corresponding Wigner distribution, eq. (25), also has Gaussian shape. The properties of coherent states are widely discussed in the litterature, see [19,20].…”

“…For example, the aspect ratio (major axis/minor axis) of the ZVS contour lines is (2q + 1)/(1 − q) which varies smoothly around q = 8/9, while the aspect ratio of the isocontours of the ground state wave-packet diverges when q → 8/9. 25 Nonwithstanding, a ZVS may be used for other purposes [144], e.g., to show the existence of an ionization threshold for the Hamiltonian (214), when ω c > ω (area coded in black in fig. 39).…”

Probabilistic and Stochastic Methods in Analysis, with Applications

“…Since atoms coherently excited by short laser pulses (Rydberg atoms) may be as large as some transistors of microelectronic ICs and the pathways between them inside the CMOS VLSI chips [10,202,203], the quantum theoretical treatment of optical holography is of particular importance for amacronics (see Section 10 infra) and nanotechnology. The linear operators I-a/at,27ti-vt' determine a representation of the Schr6dinger operators by skew-symmetric operators.…”