RESEARCH NEWS & VIEWS placed flies on a ball in a virtual-reality arena of visual displays, and fixed the insects’ heads in place. The flies explored the arena by walking on the ball, and the authors monitored turning behaviour (calculated from the ball’s movements) and neuronal activity. Neurons in the central complex showed highly tuned responses that encoded the fly’s orientation relative to a visual cue from the arena. The researchers showed that such orientation responses are generated by a population of highly active neurons, which together form a single ‘bump’ of neuronal activity that marks the direction in which the fly is facing relative to the visual cue. This activity bump seamlessly rotates around a ring of neurons in concert with the fly’s location relative to the cue, with changes in the cue’s location eliciting a concordant shift in the position of the activity bump. Do the orientation responses encoded by fly neurons reflect the convergence of self-motion and landmark cues, as in head-direction cells? In support of this theory, increasing the complexity of the visual cue did not affect the orientation response. This indicates that neuronal activity predominantly reflects the fly’s location relative to the visual landmark, rather than being a specific feature of the cue itself. Under normal circumstances, animals integrate both self-motion and landmark cues. However, if one type of cue is missing, the animal must rely on the other. Seelig and Jayaraman allowed flies to explore the virtual-reality arena in the dark, thus eliminating landmark cues. Orientation responses remained stable, indicating that the response can be driven by self-motion, but they drifted slowly over time, showing that the accuracy of the response depends on both types of cue. Moreover, the fact that flies preserve a neuronal memory of orientation even in the absence of the visual cue that created it demonstrates that their navigational behaviour is much more than a simple sensorimotor reflex. Thus, the current study points to many parallels between the orientation responses in flies and mammalian head-direction signals1. Both show increased activity when the animal faces a particular direction, irrespective of its location at the time. Both are maintained by internal self-motion cues, with familiar visual cues establishing each cell’s directionality 3. And, as in flies, orientation in rodents remains coherent in the dark, but drifts slowly over time4,5. These similarities demonstrate the sophistication of the insect navigational system. The mammalian system is thought to help generate an internal representation of space by acting as a neuronal compass (Fig. 1)6. The possibility that the fly brain contains at least one of the components needed to create a similar cognitive map is intriguing. This study also improves our understanding of the mechanisms underlying orientation responses in both invertebrates
and vertebrates. Head-direction cells are hypothesized 5 to arise from networks of neurons, dubbed ‘attractor networks’. These networks are thought to adopt a ring-like architecture that allows a single activity bump to move around the network in concert with an animal’s movement. Although some evidence consistent with this hypothesis has been observed in the past year in small numbers of rodent neurons7,8, large-scale dynamics remain difficult to observe in mammalian neuronal networks. Seelig and Jayaraman observe classic traits of a ring-like attractor network in flies, including coherent activity in the absence of visual inputs, and slow error accumulation9 — some of the most direct evidence to date for attractor networks as the mechanism that generates orientation responses. The possibility that ring-like attractor networks are evolutionarily conserved raises the exciting prospect that similar internal computational principles are used to calculate orientation in disparate species. However, the role of self-motion compared to translational movement — movement of an animal’s body position through the environment relative to the cue — in driving orientation responses remains a mystery. In rodents, head-direction responses remain coherent despite translational movement. For example, if a head-direction cell becomes established as north-preferring in response to a visual cue to the northeast, it will remain tuned to the north even if the animal moves such that the visual cue is now to its southeast. The flies in Seelig and Jayaraman’s preparation, however, do not experience this type of translational movement, because the fly’s body position relative to the cue remains fixed owing to the design of the virtual-reality system. It will be interesting to determine how fly orientation neurons respond to translation.
The authors’ work provides insight into the neuronal basis of navigation. It was already known that insects use path integration10, use polarized light to orient relative to the Sun11 and show behaviours indicative of spatial memory12. But Seelig and Jayaraman provide the first evidence for one of the components required to construct a cognitive map — a computation previously thought the preserve only of vertebrates. This finding paves the way for dissecting the neuronal basis of navigation by leveraging the powerful genetic tools and tractable neuronal circuits available in flies. ■ Thomas R. Clandinin and Lisa M. Giocomo are in the Department of Neurobiology, Stanford University, Stanford, California 94305, USA. e-mail: [email protected]; [email protected] 1. Taube, J. S., Muller, R. U. & Ranck, J. B. Jr J. Neurosci. 10, 420–435 (1990). 2. Seelig, J. D. & Jayaraman, V. Nature 521, 186–191 (2015). 3. Taube, J. S., Muller, R. U. & Ranck, J. B. Jr J. Neurosci. 10, 436–447 (1990). 4. Goodridge, J. P., Dudchenko, P. A., Worboys, K. A., Golob, E. J. & Taube, J. S. Behav. Neurosci. 112, 749–761 (1998). 5. Skaggs, W. E., Knierim, J. J., Kudrimoti, H. S. & McNaughton, B. L. Adv. Neural Inf. Process. Syst. 7, 173–180 (1994). 6. Taube, J. S. Annu. Rev. Neurosci. 30, 181–207 (2007). 7. Bjerknes, T. L., Moser, E. I. & Moser, M.-B. Neuron 82, 71–78 (2014). 8. Peyrache, A., Lacroix, M. M., Petersen, P. C. & Buzsáki, G. Nature Neurosci. 18, 569–575 (2015). 9. Zhang, K. J. Neurosci. 16, 2112–2126 (1996). 10. Wehner, R. & Srinivasan, M. V. J. Comp. Physiol. 142, 315–338 (1981). 11. Heinze, S. & Homberg, U. Science 315, 995–997 (2007). 12. Ofstad, T. A., Zuker, C. S. & Reiser, M. B. Nature 474, 204–207 (2011).
M I C R O SC O PY
Quantum control of free electrons Optical pulses have previously been used to place the electrons in the beam of an electron microscope into well-defined energy states. These electrons can now be put in a quantum superposition of those states. See Letter p.200 M AT H I E U K O C I A K
Q
uantum mechanics is a daily affair for electron microscopists. The researchers routinely focus their microscopes’ electron beams on samples to create quantum interference patterns that reveal information about the samples’ atomic and molecular
1 6 6 | NAT U R E | VO L 5 2 1 | 1 4 M AY 2 0 1 5
© 2015 Macmillan Publishers Limited. All rights reserved
structure. In an exciting paper in this issue, Feist et al.1 (page 200) demonstrate how they have used light focused on a nanostructure to make the fast electrons of one such electron beam exhibit another type of quantum behaviour — Rabi oscillations. Quantum systems have properties that their classical counterparts lack. For two-state
NEWS & VIEWS RESEARCH a
0
Occupation probability
1
1.0 0.8 N 0.6
0 1
0.4 0.2 0 Applied field (arbitrary units)
b
1 0 –1 –N
1.0 Occupation probability
N
N 0 1 2
0.8 0.6 0.4 0.2 0 Applied field (arbitrary units)
Figure 1 | Quantum superpositions. a, In a two-level system, an electron can be in either of two stationary states (0 or 1). An applied strong, oscillating electromagnetic field (black line) can put the electron into a coherent superposition of states. The probabilities of detecting the electron in either of the states oscillate with increasing strength of the field (Rabi oscillations). b, The freely propagating electrons in the electron beam of an electron microscope, such as that studied by Feist et al.1, can be placed in a large set of stationary states using an appropriately shaped electromagnetic field: state 0, which is determined by the nominal accelerating voltage of the microscope; states −1 to − N, which have the energy of state 0 minus integer multiples of the electromagnetic field’s energy; and states 1 to + N, which have the energy of state 0 plus integer multiples of the field’s energy. For a strong field, each electron is put in a superposition of these states, and the probability that the electron is in any of these states oscillates with the field strength (unconventional, multilevel Rabi oscillations). For simplicity, only a subset of the oscillations is shown. (Plot in b adapted from ref. 1.)
quantum systems, Rabi oscillations between the two, otherwise stationary, states of the system are one such property. To understand these oscillations, consider an electron in an atom that has two energy states, a ground state and an excited state (Fig. 1a). The electron will stay in one of the states forever if no external perturbation is applied to it. But if, for example, an electromagnetic field is applied to the system, the probability of finding the electron in either of the states will oscillate with time and the strength of the electromagnetic field: these are the Rabi oscillations. The oscillation frequency, called the Rabi frequency, depends mainly on the strength of the perturbation. Stopping the oscillations at any time leaves the electron in a coherent quantum superposition; that is, in a combination of both stationary states at the same time. Rabi oscillations are therefore commonly used to prepare quantum systems in a superposition of states. Such superposition provides a means of encoding information in quantuminformation technologies. In the electron microscope used by Feist et al., the freely propagating electrons of the electron beam can be placed in a large set of stationary states2 (Fig. 1b). If Rabi oscillations between these states are to be observed, the probability of the electrons being in a given energy state must be measured. This probability measurement can be easily done using
an electron energy-loss spectrometer (EELS), a device that can be added to an electron microscope. It is usually used to produce a spectrum of the electron intensity that is transmitted through the sample under study as a function of the energy loss caused by scattering from the sample. The EELS spectrum of freely propagating electrons consists of peaks centred at the energy of the electrons, and measuring the height of the peaks gives the probability of finding them in these energy states. However, putting freely propagating electrons in a coherent quantum superposition is much more difficult than measuring their probabilities of being in a given state. Unlike an electron bound to an atom, a fast electron moving in free space will generally not couple to an electromagnetic field such as an optical plane wave. But it is well established that such an electron can easily couple to an evanescent wave — a wave that does not propagate but that decays exponentially with distance from the boundaries of objects, such as nanostructures, at which they are formed. Electron microscopy is regularly used for imaging optical excitations in nanostructures at high spatial resolution through the nanostructures’ evanescent fields3. By using synchronized femtosecond (1 femtosecond is 10−15 seconds) pulses of electrons and photons in an electron-microscope set-up, researchers have previously coupled photons to fast electrons through
the evanescent light field of a nanostructure (an individual carbon nanotube or a silver nanowire)2. They showed that, in such cases, electrons could absorb or emit photons many times, resulting in spectra of electron-energy loss (or gain) consisting of a series of peaks evenly spaced according to the energy of the photons. The peaks’ intensity, and thus the probability of finding an electron in a given state, decreased monotonically with the energy of the electron loss (or gain). Soon after this remarkable experiment, others predicted4 that, using a similar experimental set-up, quantum superpositions of freely propagating electron states should be observable for longer-lasting photon pulses as a series of peaks with oscillating energies of electron loss (or gain). And this is exactly what Feist et al. have demonstrated experimentally in their study. The authors observed a quantum super position of freely propagating electron states by focusing femtosecond electron pulses on a sharp, nanometre-sized gold tip illuminated by picosecond laser pulses (1 picosecond is 10−12 s). The tip turned the laser’s plane wave into an evanescent one, allowing strong coupling of the large number of freely propagating electron states. Each state’s probability, encoded in the intensity of each peak in an EELS spectrum, oscillates at its own pace, leading to unconventional, multilevel Rabi oscillations (Fig. 1b). Feist and colleagues’ experimental achievement lies largely in the development of an electron gun that generates electron pulses with high brightness. Such an electron gun allows a relatively narrow electron beam (one with a diameter of about 15 nanometres) to be formed. A wider beam would average the evanescent field in such a manner that the Rabi oscillations and the coherent quantum superposition would be lost. By experimentally introducing the field of free-electron quantum optics, this work projects free electrons into the world of quantum information — although it will be technologically demanding to transform an electron microscope into a quantum-information processor. However, as Feist et al. also demonstrated, the control of the beam’s freely propagating electrons leads to effects other than quantum superposition, including the formation of a train of attosecond (one billion-billionth of a second) electron pulses. Such pulses could find applications in ultrafast electron spectroscopy and microscopy. ■ Mathieu Kociak is at the Laboratoire de Physique des Solides, CNRS/Université Paris Sud, 91400 Orsay, France. e-mail: [email protected] 1. Feist, A. et al. Nature 521, 200–203 (2015). 2. Barwick, B., Flannigan, D. J. & Zewail, A. H. Nature 462, 902–906 (2009). 3. García de Abajo, F. J. Rev. Mod. Phys. 82, 209–275 (2010). 4. García de Abajo, F. J., Asenjo-Garcia, A. & Kociak, M. Nano Lett. 10, 1859–1863 (2010). 1 4 M AY 2 0 1 5 | VO L 5 2 1 | NAT U R E | 1 6 7
© 2015 Macmillan Publishers Limited. All rights reserved
and vertebrates. Head-direction cells are hypothesized 5 to arise from networks of neurons, dubbed ‘attractor networks’. These networks are thought to adopt a ring-like architecture that allows a single activity bump to move around the network in concert with an animal’s movement. Although some evidence consistent with this hypothesis has been observed in the past year in small numbers of rodent neurons7,8, large-scale dynamics remain difficult to observe in mammalian neuronal networks. Seelig and Jayaraman observe classic traits of a ring-like attractor network in flies, including coherent activity in the absence of visual inputs, and slow error accumulation9 — some of the most direct evidence to date for attractor networks as the mechanism that generates orientation responses. The possibility that ring-like attractor networks are evolutionarily conserved raises the exciting prospect that similar internal computational principles are used to calculate orientation in disparate species. However, the role of self-motion compared to translational movement — movement of an animal’s body position through the environment relative to the cue — in driving orientation responses remains a mystery. In rodents, head-direction responses remain coherent despite translational movement. For example, if a head-direction cell becomes established as north-preferring in response to a visual cue to the northeast, it will remain tuned to the north even if the animal moves such that the visual cue is now to its southeast. The flies in Seelig and Jayaraman’s preparation, however, do not experience this type of translational movement, because the fly’s body position relative to the cue remains fixed owing to the design of the virtual-reality system. It will be interesting to determine how fly orientation neurons respond to translation.
The authors’ work provides insight into the neuronal basis of navigation. It was already known that insects use path integration10, use polarized light to orient relative to the Sun11 and show behaviours indicative of spatial memory12. But Seelig and Jayaraman provide the first evidence for one of the components required to construct a cognitive map — a computation previously thought the preserve only of vertebrates. This finding paves the way for dissecting the neuronal basis of navigation by leveraging the powerful genetic tools and tractable neuronal circuits available in flies. ■ Thomas R. Clandinin and Lisa M. Giocomo are in the Department of Neurobiology, Stanford University, Stanford, California 94305, USA. e-mail: [email protected]; [email protected] 1. Taube, J. S., Muller, R. U. & Ranck, J. B. Jr J. Neurosci. 10, 420–435 (1990). 2. Seelig, J. D. & Jayaraman, V. Nature 521, 186–191 (2015). 3. Taube, J. S., Muller, R. U. & Ranck, J. B. Jr J. Neurosci. 10, 436–447 (1990). 4. Goodridge, J. P., Dudchenko, P. A., Worboys, K. A., Golob, E. J. & Taube, J. S. Behav. Neurosci. 112, 749–761 (1998). 5. Skaggs, W. E., Knierim, J. J., Kudrimoti, H. S. & McNaughton, B. L. Adv. Neural Inf. Process. Syst. 7, 173–180 (1994). 6. Taube, J. S. Annu. Rev. Neurosci. 30, 181–207 (2007). 7. Bjerknes, T. L., Moser, E. I. & Moser, M.-B. Neuron 82, 71–78 (2014). 8. Peyrache, A., Lacroix, M. M., Petersen, P. C. & Buzsáki, G. Nature Neurosci. 18, 569–575 (2015). 9. Zhang, K. J. Neurosci. 16, 2112–2126 (1996). 10. Wehner, R. & Srinivasan, M. V. J. Comp. Physiol. 142, 315–338 (1981). 11. Heinze, S. & Homberg, U. Science 315, 995–997 (2007). 12. Ofstad, T. A., Zuker, C. S. & Reiser, M. B. Nature 474, 204–207 (2011).
M I C R O SC O PY
Quantum control of free electrons Optical pulses have previously been used to place the electrons in the beam of an electron microscope into well-defined energy states. These electrons can now be put in a quantum superposition of those states. See Letter p.200 M AT H I E U K O C I A K
Q
uantum mechanics is a daily affair for electron microscopists. The researchers routinely focus their microscopes’ electron beams on samples to create quantum interference patterns that reveal information about the samples’ atomic and molecular
1 6 6 | NAT U R E | VO L 5 2 1 | 1 4 M AY 2 0 1 5
© 2015 Macmillan Publishers Limited. All rights reserved
structure. In an exciting paper in this issue, Feist et al.1 (page 200) demonstrate how they have used light focused on a nanostructure to make the fast electrons of one such electron beam exhibit another type of quantum behaviour — Rabi oscillations. Quantum systems have properties that their classical counterparts lack. For two-state
NEWS & VIEWS RESEARCH a
0
Occupation probability
1
1.0 0.8 N 0.6
0 1
0.4 0.2 0 Applied field (arbitrary units)
b
1 0 –1 –N
1.0 Occupation probability
N
N 0 1 2
0.8 0.6 0.4 0.2 0 Applied field (arbitrary units)
Figure 1 | Quantum superpositions. a, In a two-level system, an electron can be in either of two stationary states (0 or 1). An applied strong, oscillating electromagnetic field (black line) can put the electron into a coherent superposition of states. The probabilities of detecting the electron in either of the states oscillate with increasing strength of the field (Rabi oscillations). b, The freely propagating electrons in the electron beam of an electron microscope, such as that studied by Feist et al.1, can be placed in a large set of stationary states using an appropriately shaped electromagnetic field: state 0, which is determined by the nominal accelerating voltage of the microscope; states −1 to − N, which have the energy of state 0 minus integer multiples of the electromagnetic field’s energy; and states 1 to + N, which have the energy of state 0 plus integer multiples of the field’s energy. For a strong field, each electron is put in a superposition of these states, and the probability that the electron is in any of these states oscillates with the field strength (unconventional, multilevel Rabi oscillations). For simplicity, only a subset of the oscillations is shown. (Plot in b adapted from ref. 1.)
quantum systems, Rabi oscillations between the two, otherwise stationary, states of the system are one such property. To understand these oscillations, consider an electron in an atom that has two energy states, a ground state and an excited state (Fig. 1a). The electron will stay in one of the states forever if no external perturbation is applied to it. But if, for example, an electromagnetic field is applied to the system, the probability of finding the electron in either of the states will oscillate with time and the strength of the electromagnetic field: these are the Rabi oscillations. The oscillation frequency, called the Rabi frequency, depends mainly on the strength of the perturbation. Stopping the oscillations at any time leaves the electron in a coherent quantum superposition; that is, in a combination of both stationary states at the same time. Rabi oscillations are therefore commonly used to prepare quantum systems in a superposition of states. Such superposition provides a means of encoding information in quantuminformation technologies. In the electron microscope used by Feist et al., the freely propagating electrons of the electron beam can be placed in a large set of stationary states2 (Fig. 1b). If Rabi oscillations between these states are to be observed, the probability of the electrons being in a given energy state must be measured. This probability measurement can be easily done using
an electron energy-loss spectrometer (EELS), a device that can be added to an electron microscope. It is usually used to produce a spectrum of the electron intensity that is transmitted through the sample under study as a function of the energy loss caused by scattering from the sample. The EELS spectrum of freely propagating electrons consists of peaks centred at the energy of the electrons, and measuring the height of the peaks gives the probability of finding them in these energy states. However, putting freely propagating electrons in a coherent quantum superposition is much more difficult than measuring their probabilities of being in a given state. Unlike an electron bound to an atom, a fast electron moving in free space will generally not couple to an electromagnetic field such as an optical plane wave. But it is well established that such an electron can easily couple to an evanescent wave — a wave that does not propagate but that decays exponentially with distance from the boundaries of objects, such as nanostructures, at which they are formed. Electron microscopy is regularly used for imaging optical excitations in nanostructures at high spatial resolution through the nanostructures’ evanescent fields3. By using synchronized femtosecond (1 femtosecond is 10−15 seconds) pulses of electrons and photons in an electron-microscope set-up, researchers have previously coupled photons to fast electrons through
the evanescent light field of a nanostructure (an individual carbon nanotube or a silver nanowire)2. They showed that, in such cases, electrons could absorb or emit photons many times, resulting in spectra of electron-energy loss (or gain) consisting of a series of peaks evenly spaced according to the energy of the photons. The peaks’ intensity, and thus the probability of finding an electron in a given state, decreased monotonically with the energy of the electron loss (or gain). Soon after this remarkable experiment, others predicted4 that, using a similar experimental set-up, quantum superpositions of freely propagating electron states should be observable for longer-lasting photon pulses as a series of peaks with oscillating energies of electron loss (or gain). And this is exactly what Feist et al. have demonstrated experimentally in their study. The authors observed a quantum super position of freely propagating electron states by focusing femtosecond electron pulses on a sharp, nanometre-sized gold tip illuminated by picosecond laser pulses (1 picosecond is 10−12 s). The tip turned the laser’s plane wave into an evanescent one, allowing strong coupling of the large number of freely propagating electron states. Each state’s probability, encoded in the intensity of each peak in an EELS spectrum, oscillates at its own pace, leading to unconventional, multilevel Rabi oscillations (Fig. 1b). Feist and colleagues’ experimental achievement lies largely in the development of an electron gun that generates electron pulses with high brightness. Such an electron gun allows a relatively narrow electron beam (one with a diameter of about 15 nanometres) to be formed. A wider beam would average the evanescent field in such a manner that the Rabi oscillations and the coherent quantum superposition would be lost. By experimentally introducing the field of free-electron quantum optics, this work projects free electrons into the world of quantum information — although it will be technologically demanding to transform an electron microscope into a quantum-information processor. However, as Feist et al. also demonstrated, the control of the beam’s freely propagating electrons leads to effects other than quantum superposition, including the formation of a train of attosecond (one billion-billionth of a second) electron pulses. Such pulses could find applications in ultrafast electron spectroscopy and microscopy. ■ Mathieu Kociak is at the Laboratoire de Physique des Solides, CNRS/Université Paris Sud, 91400 Orsay, France. e-mail: [email protected] 1. Feist, A. et al. Nature 521, 200–203 (2015). 2. Barwick, B., Flannigan, D. J. & Zewail, A. H. Nature 462, 902–906 (2009). 3. García de Abajo, F. J. Rev. Mod. Phys. 82, 209–275 (2010). 4. García de Abajo, F. J., Asenjo-Garcia, A. & Kociak, M. Nano Lett. 10, 1859–1863 (2010). 1 4 M AY 2 0 1 5 | VO L 5 2 1 | NAT U R E | 1 6 7
© 2015 Macmillan Publishers Limited. All rights reserved
