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Quantum Mechanical Interference in the Field Ionization of Rydberg Atoms

Jacob Hollingsworth

Published Jan 1, 2016• 1 citation
OpenAlex

Abstract

Rydberg atoms are traditionally alkali metal atoms with their valence electron excited to a state of very large principle quantum number. They possess exaggerated properties, and are consequently an attractive area of study for physicists. An example of their exaggerated properties is seen in their response to the presence of an applied electric field. In this work, we study the energy distribution of Rydberg atoms when subjected to a dynamic electric field intended to ionize them. We excite 85Rb atoms to a superposition of the 46D5/2 |mj| = 1/2 and |mj| = 3/2 states in the presence of a small initial electric field. After a delay time, the electric field is pulsed in order to ionize the atoms. The current produced by the ejected electrons is measured. Calculations and experimental data are presented which display interference effects between the amplitude from the components of the initial superposition.

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Quantum interference in the field ionization of Rydberg atoms

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We excite ultracold rubidium atoms in a magneto-optical trap to a coherent superposition of the three $|{m}_{j}|$ sublevels of the $37{d}_{5/2}$ Rydberg state. After some delay, during which the relative phases of the superposition components can evolve, we apply an electric field pulse to ionize the Rydberg electron and send it to a detector. The electron traverses many avoided crossings in the Stark levels as it ionizes. The net effect of the transitions at these crossings is to mix the amplitudes of the initial superposition into the same final states at ionization. Similar to a Mach-Zehnder interferometer, the three initial superposition components have multiple paths by which they can arrive at ionization and, since the phases of those paths differ, we observe quantum beats as a function of the delay time between excitation and initiation of the ionization pulse. We present a fully quantum-mechanical calculation of the electron's path to ionization and the resulting interference pattern.

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The Role of Continuum States in the Field Ionization of Rydberg Atoms

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In an experiment performed by our collaborators at Bryn Mawr, we excite rubidium-85 to a coherent superposition of the different |mj| splittings of the 37d5/2 state induced by a small electric field. After waiting for some variable delay time, we apply a time-dependent electric field to ionize the atom and record the ionized current that arrives at the detector. Due to the initial superposition, we observe an interference pattern that depends on the delay time. This thesis describes my continued work with Dr. Carroll to develop a computational model of this experiment. Our initial method of determining the current involved a semi-classical approach that did not accurately describe the phase, so the more recent developments have focused on including the continuum states in our calculation.

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The outer electron of a Rydberg atom is so weakly bound to the atomic core that a relatively small electric field may cause the electron to be stripped from the atom. The field strength at which this ionization happens is strongly dependent on the state of the Rydberg atom. Pulsed electric field ionization serves, therefore, not only as a means by which a Rydberg atom may be efficiently detected, but also a means by which the state of the Rydberg atom may be analyzed.\nThe first observation of predominantly diabatic passage to field ionization of a non-hydrogenic Rydberg atom has resulted in an improved understanding of the adiabatic and diabatic ionization processes. The magnitudes of the various field ionization features have been measured and found to agree with theory, and by detailed analysis, it is now possible to label the various field ionization signal features with the appropriate (VBAR)m(,l)(VBAR) quantum numbers. A much better understanding of the laser excitation process, the Rydberg state production, and the response of the excited state to an increasing electric field has enabled measurement of some Rydberg fine-structure intervals, through observation of field ionization quantum beats.

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Spatial and temporal correlations in cold Rydberg gases

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Rydberg atoms, i.e. atoms with one or more highly excited electrons, show exaggerated properties compared to ground state atoms. For example, their energy levels are very sensitive to external electric fields (Stark effect) and they exhibit strong interatomic interactions, which can lead to a suppression of excitation known as the Rydberg blockade. The latter property makes Rydberg atoms promising candidates for quantum simulation and quantum computing. This work describes the direct observation of the excitation blockade for highly Stark-shifted Rydberg atoms induced by controllable dipole-dipole interactions. We investigate the electric field region around and above the classical ionization threshold, which is typically not considered suitable for blockade experiments. We excite Rydberg atoms in the energy region corresponding to the unperturbed 43S1/2 state at electric fields around 127V/cm out of a magneto-optically trapped cloud of 87Rb atoms with a temperature of 150 μK. We tune the dipole-dipole interaction by the applied electric field thus changing the electric dipole moment of the excited state. The position of the Rydberg atoms is detected by ionization and subsequent ion imaging; the controlled ionization of the atoms is achieved by adiabatic transfer of the Rydberg state to an ionizing state. For the spatially resolved detection of the atoms, a high resolution ion microscope for cold atoms has been developed and experimentally characterized. It features a maximum magnification of 1000 and sub-micrometer spatial resolution. A theoretical treatment of highly Stark-shifted Rydberg states is developed introducing a complex absorbing potential. It is capable of predicting the ionization rates of the Rydberg states for a wide range of electric fields and energies with only one free parameter. Together with the numerical calculations, measurements of the ionization spectra for different Rydberg states are presented. The 43S1/2 state is measured in an electric-field range from 125V/cm to 165V/cm (classical ionization limit 127V/cm), the 70S1/2 state in an electric-field range from 15V/cm to 35V/cm (classical ionization limit 16.1V/cm) and the 100S1/2 state in an electric-field range from 7V/cm to 19V/cm (classical ionization limit 3.7V/cm). Our results show an intricate energy level structure with broad, strongly ionizing states as well as sharp, nearly non-ionizing states. The numerical calculations are also used for the prediction of selective field ionization spectra and the results are used to identify Förster resonances in the Stark spectrum of the 45D5/2 state. Complementary to the spatially resolved measurements in high electric fields, the Rydberg blockade effect is also observed via the excitation number statistics at Förster resonances.

•Jan 1, 2018•0 citations

Field ionization of Rydberg atoms in a single-cycle pulse

Baozhu Yang, F. Robicheaux

We study the ionization of Rydberg atoms in a single-cycle-pulse electric field based on both classical and quantum calculations. The ionization-probability curve exhibits a ``ripple'' structure as a function of the pulse duration and the field amplitude. These ripple structures are found to be dependent on the angular distribution of the initial state. A large electron-emission asymmetry is observed, and the ionized electron is almost completely emitted to one side of the atom except when the pulse length is roughly one Rydberg period. In both the long-pulse and the short-pulse regimes, larger electron energy can be expected from the ionization of lower-lying Rydberg states, matching the observation in a recent experiment [S. Li and R. R. Jones, Phys. Rev. Lett. 112, 143006 (2014)]. This trend is closely related to the electron-emission asymmetry associated with the field-direction change in a single-cycle pulse. The possible implications of the different energy transfer in a single-cycle pulse from that in a multicycle pulse are also discussed briefly for the strong-field ionization of the ground atomic state.

Physical Review A•Apr 13, 2015•18 citations
Rydberg atoms are traditionally alkali metal atoms with their valence electron excited to a state of very large principle quantum number. They possess exaggerated properties, and are consequently an attractive area of study for physicists. An example of their exaggerated properties is seen in their response to the presence of an applied electric field. In this work, we study the energy distribution of Rydberg atoms when subjected to a dynamic electric field intended to ionize them. We excite 85Rb atoms to a superposition of the 46D5/2 |mj| = 1/2 and |mj| = 3/2 states in the presence of a small initial electric field. After a delay time, the electric field is pulsed in order to ionize the atoms. The current produced by the ejected electrons is measured. Calculations and experimental data are presented which display interference effects between the amplitude from the components of the initial superposition.
We excite ultracold rubidium atoms in a magneto-optical trap to a coherent superposition of the three ∣mj∣|{m}_{j}|∣mj​∣ sublevels of the 37d5/237{d}_{5/2}37d5/2​ Rydberg state. After some delay, during which the relative phases of the superposition components can evolve, we apply an electric field pulse to ionize the Rydberg electron and send it to a detector. The electron traverses many avoided crossings in the Stark levels as it ionizes. The net effect of the transitions at these crossings is to mix the amplitudes of the initial superposition into the same final states at ionization. Similar to a Mach-Zehnder interferometer, the three initial superposition components have multiple paths by which they can arrive at ionization and, since the phases of those paths differ, we observe quantum beats as a function of the delay time between excitation and initiation of the ionization pulse. We present a fully quantum-mechanical calculation of the electron's path to ionization and the resulting interference pattern.
In an experiment performed by our collaborators at Bryn Mawr, we excite rubidium-85 to a coherent superposition of the different |mj| splittings of the 37d5/2 state induced by a small electric field. After waiting for some variable delay time, we apply a time-dependent electric field to ionize the atom and record the ionized current that arrives at the detector. Due to the initial superposition, we observe an interference pattern that depends on the delay time. This thesis describes my continued work with Dr. Carroll to develop a computational model of this experiment. Our initial method of determining the current involved a semi-classical approach that did not accurately describe the phase, so the more recent developments have focused on including the continuum states in our calculation.
Fully quantum and classical trajectory Monte Carlo calculations are performed for a Rydberg alkali-metal atom that is kicked by a pulsed electric field. The two calculations are compared to recent experimental results through the ionization probability versus peak field strength. The energy distributions of the final electrons are compared between the two calculations. There is a qualitative difference between the classical and quantum momentum distributions which is measurable in principle. An experiment to detect the time-dependent precession of the orbital angular momentum in Cs is also proposed.
The outer electron of a Rydberg atom is so weakly bound to the atomic core that a relatively small electric field may cause the electron to be stripped from the atom. The field strength at which this ionization happens is strongly dependent on the state of the Rydberg atom. Pulsed electric field ionization serves, therefore, not only as a means by which a Rydberg atom may be efficiently detected, but also a means by which the state of the Rydberg atom may be analyzed.\nThe first observation of predominantly diabatic passage to field ionization of a non-hydrogenic Rydberg atom has resulted in an improved understanding of the adiabatic and diabatic ionization processes. The magnitudes of the various field ionization features have been measured and found to agree with theory, and by detailed analysis, it is now possible to label the various field ionization signal features with the appropriate (VBAR)m(,l)(VBAR) quantum numbers. A much better understanding of the laser excitation process, the Rydberg state production, and the response of the excited state to an increasing electric field has enabled measurement of some Rydberg fine-structure intervals, through observation of field ionization quantum beats.
Rydberg atoms, i.e. atoms with one or more highly excited electrons, show exaggerated properties compared to ground state atoms. For example, their energy levels are very sensitive to external electric fields (Stark effect) and they exhibit strong interatomic interactions, which can lead to a suppression of excitation known as the Rydberg blockade. The latter property makes Rydberg atoms promising candidates for quantum simulation and quantum computing. This work describes the direct observation of the excitation blockade for highly Stark-shifted Rydberg atoms induced by controllable dipole-dipole interactions. We investigate the electric field region around and above the classical ionization threshold, which is typically not considered suitable for blockade experiments. We excite Rydberg atoms in the energy region corresponding to the unperturbed 43S1/2 state at electric fields around 127V/cm out of a magneto-optically trapped cloud of 87Rb atoms with a temperature of 150 μK. We tune the dipole-dipole interaction by the applied electric field thus changing the electric dipole moment of the excited state. The position of the Rydberg atoms is detected by ionization and subsequent ion imaging; the controlled ionization of the atoms is achieved by adiabatic transfer of the Rydberg state to an ionizing state. For the spatially resolved detection of the atoms, a high resolution ion microscope for cold atoms has been developed and experimentally characterized. It features a maximum magnification of 1000 and sub-micrometer spatial resolution. A theoretical treatment of highly Stark-shifted Rydberg states is developed introducing a complex absorbing potential. It is capable of predicting the ionization rates of the Rydberg states for a wide range of electric fields and energies with only one free parameter. Together with the numerical calculations, measurements of the ionization spectra for different Rydberg states are presented. The 43S1/2 state is measured in an electric-field range from 125V/cm to 165V/cm (classical ionization limit 127V/cm), the 70S1/2 state in an electric-field range from 15V/cm to 35V/cm (classical ionization limit 16.1V/cm) and the 100S1/2 state in an electric-field range from 7V/cm to 19V/cm (classical ionization limit 3.7V/cm). Our results show an intricate energy level structure with broad, strongly ionizing states as well as sharp, nearly non-ionizing states. The numerical calculations are also used for the prediction of selective field ionization spectra and the results are used to identify Förster resonances in the Stark spectrum of the 45D5/2 state. Complementary to the spatially resolved measurements in high electric fields, the Rydberg blockade effect is also observed via the excitation number statistics at Förster resonances.
We study the ionization of Rydberg atoms in a single-cycle-pulse electric field based on both classical and quantum calculations. The ionization-probability curve exhibits a ``ripple'' structure as a function of the pulse duration and the field amplitude. These ripple structures are found to be dependent on the angular distribution of the initial state. A large electron-emission asymmetry is observed, and the ionized electron is almost completely emitted to one side of the atom except when the pulse length is roughly one Rydberg period. In both the long-pulse and the short-pulse regimes, larger electron energy can be expected from the ionization of lower-lying Rydberg states, matching the observation in a recent experiment [S. Li and R. R. Jones, Phys. Rev. Lett. 112, 143006 (2014)]. This trend is closely related to the electron-emission asymmetry associated with the field-direction change in a single-cycle pulse. The possible implications of the different energy transfer in a single-cycle pulse from that in a multicycle pulse are also discussed briefly for the strong-field ionization of the ground atomic state.