Transfer of optical orbital angular momentum to a bound electron

Abstract

Photons can carry angular momentum, not only due to their spin, but also due to their spatial structure. This extra twist has been used, for example, to drive circular motion of microscopic particles in optical tweezers as well as to create vortices in quantum gases. Here we excite an atomic transition with a vortex laser beam and demonstrate the transfer of optical orbital angular momentum to the valence electron of a single trapped ion. We observe strongly modified selection rules showing that an atom can absorb two quanta of angular momentum from a single photon: one from the spin and another from the spatial structure of the beam. Furthermore, we show that parasitic ac-Stark shifts from off-resonant transitions are suppressed in the dark centre of vortex beams. These results show how light's spatial structure can determine the characteristics of light-matter interaction and pave the way for its application and observation in other systems.

ARTICLE

Received 2 Feb 2016 | Accepted 23 Aug 2016 | Published 3 Oct 2016

Photons can carry angular momentum, not only due to their spin, but also due to their spatial structure. This extra twist has been used, for example, to drive circular motion of microscopic particles in optical tweezers as well as to create vortices in quantum gases. Here we excite an atomic transition with a vortex laser beam and demonstrate the transfer of optical orbital angular momentum to the valence electron of a single trapped ion. We observe strongly modied selection rules showing that an atom can absorb two quanta of angular momentum from a single photon: one from the spin and another from the spatial structure of the beam. Furthermore, we show that parasitic ac-Stark shifts from off-resonant transitions are suppressed in the dark centre of vortex beams. These results show how lights spatial structure can determine the characteristics of lightmatter interaction and pave the way for its application and observation in other systems.

DOI: 10.1038/ncomms12998 OPEN

Transfer of optical orbital angular momentum to a bound electron

Christian T. Schmiegelow1,w, Jonas Schulz1, Henning Kaufmann1, Thomas Ruster1, Ulrich G. Poschinger1

& Ferdinand Schmidt-Kaler1

1 QUANTUM, Institut fr Physik, Universitat Mainz, Staudingerweg 7, 55128 Mainz, Germany. w Present address: Departamento de Fsica, FCEyN, UBA and IFIBA, Conicet, Pabelln 1, Ciudad Universitaria, 1428 Buenos Aires, Argentina. Correspondence and requests for materials should be addressed to C.T.S.

(email: mailto:[email protected]

Web End [email protected] ).

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The interaction between light and matter is governed by symmetries from which conservation laws of energy, momentum and angular momentum emerge. For example,

the sense of rotation of the polarization of a photon along its propagation axis determines the torque it can exert on matter. This phenomenon is known to occur on macroscopic1,2 as well as on atomic scales3. At a macroscopic level, the polarization of light can be used to rotate large objects as well as micrometer-sized particles. On an atomic level, the polarization of light can change the angular momentum of bound electrons. This is expressed in the form of selection rules, which indicate which changes of angular momentum of the atom are possible when it interacts with a photon.

Specially structured light beams can have extra angular momentum associated with their spatial mode structure4. In particular, LaguerreGaussian LGlp beams carry an additional orbital angular momentum (OAM) of l per photon5,6. Laguerre

Gaussian beams have been proposed and employed for numerous novel applications such as high-dimensional quantum information7, quantum cryptography8 and quantum memories9. Also, OAM-carrying beams of electrons10, neutrons11 and electromagnetic terahertz radiation12 have been demonstrated.

Light beams with OAM have been used to drive motion of microscopic particles in optical tweezers as well as to generate vortices in degenerate quantum gases13,14. Up to date, however, it was not clear if this extra angular momentum could affect the state of motion of bound electrons, that is, change the standard selection rules of optical excitation. This issue was debated during the last two decades1525, and rst experiments2628 did not observe these effects.

Electromagnetically driven transitions between two atomic states occur if the superposition of their charge distributions match the multipole structure of the exciting eld29. This allows for categorizing atomic transitions in dipolar, quadrupolar and higher orders: a dipole transition is driven by an oscillating eld, a quadrupole one is driven by an oscillating eld gradient and so on. Quadrupole transitions, driven by eld gradients occurring in optical beams, are particulary interesting for they can even occur where there is no light intensity but only eld gradient30.

As travelling waves, optical beams have a longitudinal eld gradient, which allows for driving electric quadrupole transitions31. A transverse gradient, due to the spatial structure of the beam front, can drive quadrupole transitions too. In particular, the centre of LG10 beams exhibit a strong eld gradient, where the intensity vanishes.

In this work, we report the observation of transfer of optical OAM from a vortex LG10 beam to the motion of the valence electron of a trapped ion. In particular, we measure strongly modied selection rules accounting for OAM associated with the spatial structure of the beam. We observe strong excitation in the dark penumbra near the centre of the beam, driven solely by the transverse eld gradient. In such conditions, we also observe strong suppression from parasitic ac-Stark shifts of off-resonant transitions.

ResultsStructured beams interacting with a single trapped ion. For the experimental investigation of the interaction of structured light with the internal degrees of freedom of atoms, we use a single laser-cooled 40Ca ion trapped in a microstructured segmented

Paul trap with a thermal spatial spread of B60 nm (see Fig. 1). Precise sub-nanometer positioning of the ion along the structured beam is achieved by changing the voltages of the trapping electrodes32.

A continuous-wave laser near 729 nm is used to drive the 42S1/2232D5/2 quadrupole transition. As indicated in Fig. 1, this laser is shaped to the transverse LG00, LG 10 and LG 20 modes by holographic plates33 and focused onto the ion with a beam waist of w0 2.7(2) mm.

To measure the interaction strength, the ion is rst initialized by optical pumping on one of the 42S1/2 sublevels (see Methods

section). Upon exposure to the optical eld on resonance with the quadrupole transition, the internal state of the ion undergoes coherent oscillations between the ground and excited state, which are measured by state-dependent uorescence. The Rabi frequency O of these oscillations is measured to quantify the coupling strength. Each Zeeman-split sublevel of the 42S1/2232D5/2 transition is spectroscopically resolved due to an external magnetic eld of 13 mT, allowing to probe all transitions 42S1=2; mJ 12

$ 32D5=2; mJ 12 ; 32 ; 52

independently by tuning the laser to the respective resonance (see Methods section for more details).

Modication of transition selection rules with light OAM. We demonstrate the joint transfer of a quantum of OAM and spin

a b

Figure 1 | Energy levels and experimental set-up. (a) Energy levels in

40Ca . The quadrupole transition at 729 nm is used to investigate the transfer of OAM from a photon to a single ion, the dipole transitions near 397, 866 and 854 nm are used for cooling, initialization and detection. (b) Experimental set-up. A single ion is trapped in a linear segmented Paul trap (yellow) inside an UHV chamber (gray). Delivered through bres (top-left), light resonant with the dipole transitions is used for Doppler cooling, detection (397 and 866 nm) and state reset (854 nm). Resonance uorescence near 397 nm is imaged on an EMCCD camera (bottom-right) with lenses L2,3, passing a dichroic mirror and an interference lter. To excite the quadrupole 42S1/2232D5/2 transition, coherent light from a Ti:Sa laser is transmitted through an acousto-optic modulator for frequency and timing control, ltered by a polarization maintaining bre and converted to the desired vortex beam with a holographic phase plate. The laser beam polarization is set by a series of quarter- and half-wave plates, and focused onto the ion by lenses L1 (f 50 mm) and L2 (f 67 mm). The magnetic

eld is controlled by coils C14 plus an additional coil (not shown) in the vertical direction.

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angular momentum (SAM) from the optical eld to the ion. For this, we choose a setting with rotational symmetry about the propagation axis z of the 729 nm beam. This is achieved by aligning the magnetic eld along the z-direction and placing the ion in the beam centre, at the bright centre for the Gaussian LG00 beam or at the dark penumbra for the LG 10 beams, respectively.

For this geometry, the angular momentum projection along z is a conserved quantity, which enforces that transitions are allowed only if the total angular momentum mph of the photon matches the difference in angular momentum projection Dm between initial and nal atomic states. The photons total angular momentum mph is given by the sum of SAM (for circular polarization s 1) and OAM (l 0 for LG00 and l 1 for

LG 10) modes.

We verify that OAM contributes to angular momentum conservation by measuring the Rabi frequency for all possible values of mph and Dm. We indeed observe coherent Rabi oscillations in all cases where angular momentum conservation is fullled: for Dm 0, an OAM of 1 compensates for a SAM of

81, whereas for Dm 2, OAM and SAM add up. In Fig. 2, the

results for initialization in the 42S1=2; mJ 12

state are shown.

One clearly sees that the interaction strength for all the cases when mph Dm is stronger than when it is not (analogous results

obtained for the opposite spin initialization are presented in the Supplementary Table 2).

For the transitions driven by the LG00 (Gaussian) beam, the power-normalized Rabi frequencies are measured to be 13.0(8)

times stronger than those driven by the LG 10 (vortex) beams. This is consistent with the expected relative strength21 for the measured beam waist, as determined by the ratio of waist to optical wavelength: pw0/l 12.6(3). Additionally, the relative

coupling strengths of different transitions are governed by the WignerEckart theorem to account for coupling of SAM and OAM. For all transitions where angular momentum conservation is not fullled, that is, where Dmamph, the measured coupling strengths are below 3% of the coupling strengths measured for the mph Dm 1 transitions, consistent with our error estimations

(see Methods section).

For the case of an LG 20 beam, we observewithin our experimental precisionnegligible excitation for all transitions

(kHz/W)

a

c

Spin

Orbital AM

1 +1

0

+

1/2

mJ=5/2 3D5/2

AM 4 3 2 1 0

4 3 2 1 0

4 3 2 1 0

(kHz/W)

40 30

30 20

20

10

+1/2

b

mJ=1/2

+3/2 +5/2

+1/2

0

10

0

2

1

=2

0 m

1

mph

40 30 20 10

0

=0

mph=1

mph=2

=2

2

d

1.0

3D 5/2 state population

0.5

2 1 0 1 2

0.0 0.0 0.2 0.4 0.6 0.8 1.0

m

t (ms/W)

Figure 2 | Transition selection rules. (a) Energy-level structure for the 42S1/2232D5/2 manifold, indicating which eld structure and polarization drives each transition. Yellow (blue) indicates polarization s( ); clockwise (anticlockwise) curl indicates vortex LG10 LG 10

beams, dot indicates a Gaussian LG00 beam. (b,c) Interaction strength as Rabi frequencies for all spin and OAM combinations and for all possible transitions, normalized to 1 mW of laser power. (d) Example measurement data corresponding to s, Dm 0 and all three beam combinations, indicated by the yellow stripe in (c). For all

experiments, a total exposure time of 200 ms was scanned in steps of 5 ms for varying optical powers in the 360 mW range to determine the corresponding Rabi frequencies. Numerical values for these plots are available in the Supplementary Table 1. The corresponding raw data is available as supplementary material and its evaluation is detailed in Supplementary Note 1.

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and polarization combinations. This is due to the fact that at the penumbra of the LG20, the eld amplitude increases quadratically in the radial direction. Thus, the quadrupole transitionwhich is driven by eld gradientscannot be excited at the centre of an LG 20 beam.

Beam proles. We use the ion as a localized eld probe34,35 to map out the transverse and longitudinal eld gradients for the LG00, LG10 and LG20 beams by transversely moving the ion through the focus, see Fig. 3. Here we choose the magnetic eld at 45 with respect to the propagation direction z of the 729 nm beam, which is now linearly polarized. We probe the Dm 1 transition,

where the excitation mechanism is controlled by the optical polarization21 for this setting: if the electric eld is vertically (V) polarized (orthogonal to the plane spanned by magnetic eld and beam propagation direction), the excitation strength is determined by the longitudinal gradient, proportional to the local intensity. By contrast, for horizontal (H) polarization, the coupling strength is given by the transverse gradient.

For each of the LG beams, we observe that the Rabi frequency measurement with V polarization reproduces the respective eld amplitude prole, that is, the coupling strength is proportional to the square root of the laser intensity. Conversely, for the case of the measurements with H polarization, the strength of the transverse gradient is mapped out. At the penumbra of the LG10 vortex beam (Fig. 3b), the coupling mediated by the transverse gradient exceeds the one corresponding to the longitudinal gradient case by 6 s.d., that is, the ion is actually excited in the dark. We name these dark regions of an optical beam, where the effects of its gradient can be stronger than those due to the local intensity, the penumbra. This is not to be confused with the vortex or quantum core36. In fact, it is in the penumbra of the LG10 where the Dm 0, 2 transitions were

driven in the previous experiment.

By contrast, for the LG 20, we observe that both longitudinal- and transverse-gradient-driven excitations are below our sensitivity limit at the central penumbra of the beam, see Fig. 3c. These results show, as mentioned before, that at the centre of this beam both the electric eld amplitude and its transverse gradient vanish.

a

300

400

100

0

/2 (kHz/mW)

/2 (kHz/mW)

/2 (kHz/mW)

200

100

0

b

300

200

c

400

100

0

300

200

10

5

0 5 10

Ion axial position (m)

Figure 3 | Beam proles. Excitation proles in units of power-normalized Rabi frequency as a function of the ion position across three different beams: (a) LG00 (Gaussian), (b) LG10 and (c) LG20. Red (blue) data points correspond to V (H) polarization, that is, to excitation driven by the longitudinal (transverse) eld gradient. Fits (solid lines) correspond to ideal LG beam intensity proles (red) and their respective transverse eld gradients (blue). The insets show beam intensity images taken with a CCD camera placed before the focusing lenses, revealing the same non-ideal LG outer ring structure as measured with the ion. Note that in b, it can be clearly seen that the ion can be excited if it is in the dark penumbra of the LG10 vortex beam. The measurements of the ac-Stark shift are carried out at positions marked A and B. Raw data as well as evaluation are can be referenced from Supplementary

Note 2 and found as Supplementary Data.

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The outer shoulders observed in the measurements represent deviations from ideal LaguerreGaussian beam proles. We conrm this by imaging the beam proles on a CCD camera before the focusing lenses. The corresponding outer rings are clearly observed, see insets in Fig. 3. These beam imperfections result from bre out-coupling and diffraction on the holographic plates generating the LG beams.

For all three cases, beam-centre alignment is done with respect to the central feature of the longitudinal gradient. This feature is sharper for the LG10 beam than for LG00 and LG20, leading to slight miss-alignment of the longitudinal with respect to transverse gradients for these cases.

AC-Stark shift suppression. An important challenge for the operation of laser-driven atomic qubits37 as well as for the implementation of optical frequency standards38 is the mitigation of ac-Stark shifts. These are caused by off-resonant coupling of the probe beam to parasitic atomic transitions. In our setting, the ac-Stark shifts are mainly generated either by off-resonant driving of the quadrupole transition, or by far off-resonant coupling to the 42S1/2242P1/2, 42S1/2242P3/2 and 32D5/2242P3/2 dipole transitions. The quadrupolar ac-Stark shift can be eliminated by polarization and magnetic eld alignment, or by additional compensation beams. Here we demonstrate that dipolar shifts are substantially suppressed in the penumbra of a vortex beam, whereas the coherent coupling persists.

We measure the energy shift DS caused by the 729 nm beam in the LG10 vortex mode, which is red detuned by D 2p 25 MHz

with respect to the 42S1=2; mJ 12

$ 32D5=2; mJ 32

transition. This is done by carrying out a Ramsey experiment, where a superposition of these two states acquires a phase f DS t (ref. 37) upon exposure to the beam at power PD for

time t (see Methods section). We compare the results for case A, where the ion is placed in the penumbra of the H polarized beam, and for case B, where the ion is placed at the intensity maximum of the side lobe of the V polarized beam, as marked in Fig. 3b). In case A, the transition is driven in the dark by the transverse gradient, whereas for case B, it is driven by the longitudinal gradient, and the ion is exposed to a high intensity. At position A, we measure an ac-Stark shift of DS 2p 1.54(15) kHz

at a power of PD 7.50(15) mW and a Rabi frequency

O 2p 11.93(24) kHz at a power of PD 20(1) mW. At

position B, we measure an ac-Stark shift of DS 2p 19.1(1)

kHz at a power of PD 1.75(4) mW and a Rabi frequency

O 2p 15.67(31) kHz at a power of PD 2.6(1) mW.

From the measured values for the ac-Stark shift, the power-normalized quadrupolar contribution is subtracted, that is, D0S DS PD=PO

O2= 2D

. Additionally, the values are nor

malized by overall optical power PD. The corrected, normalized

shift in case A is determined to be 0.70(25)% of the corresponding value for case B. This residual shift is attributed to thermal uctuations of the ion position into regions of non-zero eld amplitude (see Methods section). Moreover, we compare the power-normalized ratios of the residual dipolar shift to the respective Rabi frequency. The quantity x D0SP 1D

=OP

state at a delity \99%.

Coupling strength determination sequence. Each sequence starts with Doppler laser cooling, followed by optical pumping into either of the two ground-state sublevels 42S1=2; mS 12

. Next, the probe pulse near 729 nm is applied for

driving Rabi oscillations between the ground state and the metastable 32D5/2 state.

The nal state is determined from observing state-dependent uorescence on an EMCCD camera, whereas illuminating the ion near 397 and 866 nm. Observation of uorescence indicates the ion to be in the S1/2 state, whereas absence of uorescence indicates a collapse into the 32D5/2 state. Before the sequence is repeated, we apply light near 854 nm to remove population from the 32D5/2 manifold, see Fig. 1. By repeating this sequence 200 times, we obtain an estimate of the 32D5/2 state occupation probability. By measuring this excitation probability versus the probe pulse duration, ranging up to a few hundred ms, we determine the Rabi frequency O.

Error estimation on the coupling strengths. Small residual excitation measured on forbidden transitions, where Dmamph, is attributed to three effects: thermal position uctuations of the ion, imperfect optical polarization and a non-zero angle between the magnetic eld and the laser propagation direction. The thermal position spread is most prominent on the transitions involving the vortex beam due to its sharp transverse structure (mph 0, 2, see Fig. 2c). To estimate the

excess excitation, we calculate the overlap between the beams eld prole with the ions thermal position spread. This spread is given by about 60 nm, as independently measured for our experimental conditions of a Doppler-cooled

40Ca ion. Consistent with these estimations, all spurious couplings observed are below 3% of the coupling strength pertaining to the mph Dm 1 transition.

Stark shift determination sequence. State preparation and read-out are carried out as for the sequence before. After preparation, the ion located either at the penumbra or at the intensity maximum is exposed to the probe beam resonant to the 42S1=2; mJ 12

$ 32D5=2; mJ 32

1=2 O

is a suitable gure-of-merit, as it gives the ratio of the undesired shift to the desired coherent coupling when multiplied with the square root of the employed optical power. For the transverse-gradient-driven excitation in the dark, we nd a suppression by xA/xB 2.5(9)% as compared with the long-

itudinal-gradient-driven case.

DiscussionOur results open up a realm of future research directions, in which OAM of light can be harnessed as an extra control

parameter in lightmatter interaction. The key aspects in our study are the use of a quadrupole transition, focusing the probe beam close to the diffraction limit and using a well-localized atomic system. Determining which of these conditions are sufcient to observe enhanced effects due to the structure of the beam is a prerequisite for extending this technique to other physical systems as well as for possible applications. These include the mapping of high-dimensional ying qubits from photons to atomic quantum memories7, tailored interactions to improve quantum logic gates37, the control of quantized motion of trapped particles21,22, the suppression of ac-Stark shifts for optical clock transitions38 and the excitation of high OAM Rydberg states39, exciting molecule complexes40 as well as in articial atoms41.

Methods

Optical pumping. For the beam prole reconstructions and the ac-Stark shift experiments, where the magnetic eld was at 45 with respect to the 729 nm beam, optical pumping was carried out with s polarized light driving the 42S1/2242P1/2

dipole transition near 397 nm. For the experiments on the determination of the transition selection rules, the 729 nm beam is aligned parallel to the magnetic eld. Here pumping is carried out by transferring population from the 42S1/2 levels to be depleted to a 32D5/2 level, and then resetting the population to the 42S1/2 manifold with light resonant on the 32D5/2242P3/2 transition near 854 nm, see Fig. 1. By repeating this sequence 10 times, we can prepare the desired 42S1=2; mJ 12

transition at a pulse area of p/2, such

that a balanced superposition of both states is created. Next, it is exposed to the off-resonant vortex beam for time t, which induces an ac-Stark phase shift on the superposition. Finally, a second resonant p/2 pulse is applied. After recording the nal population in the excited state versus t, the ac-Stark shift is determined by the frequency of the resulting coherent oscillations.

Data availability. The authors declare that the main data supporting the ndings of this study are available within the article and its Supplementary Information les. Extra data are available from the corresponding author upon request.

References

1. Beth, R. A. Mechanical detection and measurement of the angular momentum of light. Phys. Rev. 50, 115125 (1936).

2. Friese, M. E. J., Nieminen, T. A., Heckenberg, N. R. & Rubinsztein-Dunlop, H. Optical alignment and spinning of laser-trapped microscopic particles. Nature 394, 348350 (1998).

NATURE COMMUNICATIONS | 7:12998 | DOI: 10.1038/ncomms12998 | http://www.nature.com/naturecommunications

Web End =www.nature.com/naturecommunications 5

ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms12998

3. Kastler, A. Optical methods for studying hertzian resonances. Science 158, 214221 (1967).

4. Allen, L., Beijersbergen, M. W., Spreeuw, R. J. C. & Woerdman, J. P. Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes. Phys. Rev. A 45, 81858189 (1992).

5. Torres, J. P. & Torner., L. Twisted Photons: applications of Light with Orbital Angular Momentum (Wiley, 2011).

6. Andrews, D. L. & Babiker., M. The Angular Momentum of Light (Cambridge University Press, 2013).

7. Fickler, R. et al. Interface between path and orbital angular momentum entanglement for high-dimensional photonic quantum information. Nat. Commun. 5, 4502 (2014).

8. Souza, C. E. R. et al. Quantum key distribution without a shared reference frame. Phys. Rev. A 77, 032345 (2008).

9. Nicolas, A. et al. A quantum memory for orbital angular momentum photonic qubits. Nat. Photonics 8, 234238 (2014).

10. Verbeeck, J., Tian, H. & Schattschneider, P. Production and application of electron vortex beams. Nature 467, 301304 (2010).

11. Clark, C. W. et al. Controlling neutron orbital angular momentum. Nature 525, 504506 (2015).

12. He, J. et al. Generation and evolution of the terahertz vortex beam. Opt. Express

21, 20230 (2013).

13. He, H., Friese, M. E. J., Heckenberg, N. R. & Rubinsztein-Dunlop, H. Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity. Phys. Rev. Lett. 75, 826829 (1995).

14. Andersen, M. F. et al. Quantized rotation of atoms from photons with orbital angular momentum. Phys. Rev. Lett. 97, 170406 (2006).

15. Van Enk, S. J. & Nienhuis, G. Commutation rules and eigenvalues of spin and orbital angular momentum of radiation elds. J. Mod. Opt, 41, 963977 (1994).

16. Babiker, M., Bennett, C. R., Andrews, D. L. & Dvila Romero, L. C. Orbital angular momentum exchange in the interaction of twisted light with molecules. Phys. Rev. Lett. 89, 143601 (2002).

17. Jauregui, R. Rotational effects of twisted light on atoms beyond the paraxial approximation. Phys. Rev. A 033415, 033415 (2004).

18. Andrews, D. L., Romero, L. C. D. & Babiker, M. On optical vortex interactions with chiral matter. Opt. Commun. 237, 133139 (2004).

19. Klimov, V., Bloch, D., Ducloy, M. & Leite, J. R. R. Detecting photons in the dark region of Laguerre-Gauss beams. Opt. Express 17, 9718 (2009).

20. Tang, Y. & Cohen, A. E. Optical chirality and its interaction with matter. Phys. Rev. Lett. 104, 14 (2010).

21. Schmiegelow, C. T. & Schmidt-Kaler, F. Light with orbital angular momentum interacting with trapped ions. Eur. Phys. J. D 66, 19 (2012).

22. Mondal, P. K., Deb, B. & Majumder, S. Angular momentum transfer in interaction of Laguerre-Gaussian beams with atoms and molecules. Phys. Rev. A 89, 2933 (2014).

23. Scholz-Marggraf, H. M., Fritzsche, S., Serbo, V. G., Afanasev, A. & Surzhykov, A. Absorption of twisted light by hydrogenlike atoms. Phys. Rev. A 90, 013425 (2014).

24. Afanasev, A., Carlson, C. E. & Mukherjee, A. High-multipole excitations of hydrogen-like atoms by twisted photons near a phase singularity. J. Opt. 18, 074013 (2016).

25. Peshkov, A. A., Serbo, V. G., Fritzsche, S. & Surzhykov, A. Absorption of twisted light by a mesoscopic atomic target. Phys. Scripta 91, 064001 (2016).

26. Araoka, F., Verbiest, T., Clays, K. & Persoons, A. Interactions of twisted light with chiral molecules: an experimental investigation. Phys. Rev. A 71, 055401 (2005).

27. Lfer, W., Broer, D. J. & Woerdman, J. P. Circular dichroism of cholesteric polymers and the orbital angular momentum of light. Phys. Rev. A 83, 065801 (2011).

28. Mathevet, R., de Lesegno, B. V., Pruvost, L. & Rikken, G. L. J. A. Negative experimental evidence for magneto-orbital dichroism. Opt. Express 21, 39413945 (2013).

29. Rochester, S. M. & Budker, D. Atomic polarization visualized. Am. J. Phys. 69, 450 (2001).

30. Mundt, A. B. et al. Coherent coupling of a single 40Ca ion to a high-nesse optical cavity. Appl. Phys. B 76, 117124 (2003).

31. Sauter, T. H., Neuhauser, W., Blatt, R. & Toschek, P. E. Observation of quantum jumps. Phys. Rev. Lett. 57, 16961698 (1986).

32. Schulz, S. A., Poschinger, U., Ziesel, F. & Schmidt-Kaler., F. Sideband cooling and coherent dynamics in a microchip multi-segmented ion trap. New J. Phys. 10, 045007 (2008).

33. Mair, A., Vaziri, A., Weihs, G. & Zeilinger, A. Entanglement of the orbital angular momentum states of photons. Nature 412, 313316 (2001).

34. Guthhrlein, G. R., Keller, M., Hayasaka, K., Lange, W. & Walther., H. A single ion as a nanoscopic probe of an optical eld. Nature 414, 4951 (2001).

35. Horak, P. et al. Optical kaleidoscope using a single atom. Phys. Rev. Lett. 88, 043601 (2002).

36. Berry, M. V. & Dennis, M. R. Quantum cores of optical phase singularities.J. Opt. A 6, S178 (2004).37. Haffner, H. et al. Precision measurement and compensation of optical stark shifts for an ion-trap quantum processor. Phys. Rev. Lett. 90, 143602 (2003).

38. Ludlow, A. D., Boyd, M. M., Ye, J., Peik, E. & Schmidt, P. O. Optical atomic clocks. Rev. Mod. Phys. 87, 637701 (2015).

39. Rodrigues, J. D., Marcassa, L. G. & Mendona, J. T. Excitation of high orbital angular momentum rydberg states with laguerre-gauss beams. J. Phys. B 49, 074007 (2016).

40. Germann, M., Tong, X. & Willitsch, S. Observation of electric-dipole-forbidden infrared transitions in cold molecular ions. Nat. Phys. 10, 820824 (2014).

41. Quinteiro, G. F. & Tamborenea, P. I. Electronic transitions in disk-shaped quantum dots induced by twisted light. Phys. Rev. B 79, 155450 (2009).

Acknowledgements

We thank Rupert Ursin and Anton Zeilinger for lending us the holographic phase plates;

A. Wiens and A. Walther for contributions on early stages of the experiment;

S. Franke-Arnold and D. Budker for useful comments; and A. Z. Khoury for inspiring

this work with a lecture on orbital angular momentum of photons at the J. A. Swieca

School in 2008 in Sao Paulo. C.T.S. acknowledges the support of the Alexander von

Humboldt Foundation.

Author contributions

C.T.S. and F.S.-K. conceived the idea of the experiment. Experimental data were taken

by C.T.S. and J.S, using an apparatus primarily set up by C.T.S., J.S., H.K. and T.R.

Data analysis was performed by C.T.S., J.S. and U.G.P. The paper was written by C.T.S.,

F.S.-K., J.S. and U.G.P., with input from all authors.

Additional information

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How to cite this article: Schmiegelow, C. T. et al. Transfer of optical orbital angular

momentum to a bound electron. Nat. Commun. 7, 12998 doi: 10.1038/ncomms12998

(2016).

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r The Author(s) 2016

6 NATURE COMMUNICATIONS | 7:12998 | DOI: 10.1038/ncomms12998 | http://www.nature.com/naturecommunications

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