Mehul Malik

Colloquium: Understanding Quantum Weak Values: Basics and Applications

The Institute of Optics, University of Rochester, Rochester, New York 14627, USAand Department of Physics, University of Ottawa, Ottawa, Ontario, Canada(published 28 March 2014)Since its introduction 25 years ago, the quantum weak value has gradually transitioned from atheoretical curiosity to a practical laboratory tool. While its utility is apparent in the recent explosionof weak value experiments, its interpretation has historically been a subject of confusion. Here apragmaticintroductiontotheweakvalueintermsofmeasurablequantitiesispresented,alongwithanexplanation for how it can be determined in the laboratory. Further, its application to three distinctexperimental techniques is reviewed. First, as a large interaction parameter it can amplify smallsignals above technical background noise. Second, as a measurable complex value it enables noveltechniques for direct quantum state and geometric phase determination. Third, as a conditionedaverage of generalized observable eigenvalues it provides a measurable window into nonclassicalfeaturesofquantummechanics.Inthisselectivereview,asingleexperimentalconfigurationtodiscussand clarify each of these applications is used.

Communication with spatially modulated light through turbulent air across Vienna

Transverse spatial modes of light offer a large state-space with interesting physical properties. For exploiting these special modes in future long-distance experiments, the modes will have to be transmitted over turbulent free-space links. Numerous recent lab-scale experiments have found significant degradation in the mode quality after transmission through simulated turbulence and consecutive coherent detection. Here, we experimentally analyze the transmission of one prominent class of spatial modes?orbital-angular momentum (OAM) modes?through 3 km of strong turbulence over the city of Vienna. Instead of performing a coherent phase-dependent measurement, we employ an incoherent detection scheme, which relies on the unambiguous intensity patterns of the different spatial modes. We use a pattern recognition algorithm (an artificial neural network) to identify the characteristic mode patterns displayed on a screen at the receiver. We were able to distinguish between 16 different OAM mode superpositions with only a ?1.7% error rate and to use them to encode and transmit small grayscale images. Moreover, we found that the relative phase of the superposition modes is not affected by the atmosphere, establishing the feasibility for performing long-distance quantum experiments with the OAM of photons. Our detection method works for other classes of spatial modes with unambiguous intensity patterns as well, and can be further improved by modern techniques of pattern recognition.

High-dimensional quantum cryptography with twisted light

Quantum key distribution (QKD) systems often rely on polarization of light for encoding, thus limiting the amount of information that can be sent per photon and placing tight bounds on the error rates that such a system can tolerate. Here we describe a proof-of-principle experiment that indicates the feasibility of high-dimensional QKD based on the transverse structure of the light field allowing for the transfer of more than 1 bit per photon. Our implementation uses the orbital angular momentum (OAM) of photons and the corresponding mutually unbiased basis of angular position (ANG). Our experiment uses a digital micro-mirror device for the rapid generation of OAM and ANG modes at 4 kHz, and a mode sorter capable of sorting single photons based on their OAM and ANG content with a separation efficiency of 93%. Through the use of a seven-dimensional alphabet encoded in the OAM and ANG bases, we achieve a channel capacity of 2.05 bits per sifted photon. Our experiment demonstrates that, in addition to having an increased information capacity, multilevel QKD systems based on spatial-mode encoding can be more resilient against intercept-resend eavesdropping attacks.

Influence of atmospheric turbulence on optical communications using orbital angular momentum for encoding

We describe an experimental implementation of a free-space 11-dimensional communication system using orbital angular momentum (OAM) modes. This system has a maximum measured OAM channel capacity of 2.12 bits/photon. The effects of Kolmogorov thin-phase turbulence on the OAM channel capacity are quantified. We find that increasing the turbulence leads to a degradation of the channel capacity. We are able to mitigate the effects of turbulence by increasing the spacing between detected OAM modes. This study has implications for high-dimensional quantum key distribution (QKD) systems. We describe the sort of QKD system that could be built using our current technology.

Influence of atmospheric turbulence on states of light carrying orbital angular momentum

We have experimentally studied the degradation of mode purity for light beams carrying orbital angular momentum (OAM) propagating through simulated atmospheric turbulence. The turbulence is modeled as a randomly varying phase aberration, which obeys statistics postulated by Kolmogorov turbulence theory. We introduce this simulated turbulence through the use of a phase-only spatial light modulator. Once the turbulence is introduced, the degradation in mode quality results in crosstalk between OAM modes. We study this crosstalk in OAM for 11 modes, showing that turbulence uniformly degrades the purity of all the modes within this range, irrespective of mode number.

Rapid generation of light beams carrying orbital angular momentum.

We report a technique for encoding both amplitude and phase variations onto a laser beam using a single digital micro-mirror device (DMD). Using this technique, we generate Laguerre-Gaussian and vortex orbital-angular-momentum (OAM) modes, along with modes in a set that is mutually unbiased with respect to the OAM basis. Additionally, we have demonstrated rapid switching among the generated modes at a speed of 4 kHz, which is much faster than the speed regularly achieved by phase-only spatial light modulators (SLMs). The dynamic control of both phase and amplitude of a laser beam is an enabling technology for classical communication and quantum key distribution (QKD) systems that employ spatial mode encoding.

Twisted light transmission over 143 km

Significance Light is the main carrier of information. Its spatial mode allows the encoding of more than 1 bit per photon, and thus can increase the information capacity. For communication purposes, these modes need to be transmitted over large distances. Nowadays, fiber-based solutions are in their infancy, which renders free-space transmission the only possibility. We present an experiment where we investigate the behavior of the spatial modes after a distance of 143 km. With the help of an artificial neural network, we distinguished different mode superpositions up to the third order with more than 80% accuracy. Our results indicate that with state-of-the-art adaptive optics systems, both classical communication and entanglement transmission is feasible over distances of more than 100 km. Spatial modes of light can potentially carry a vast amount of information, making them promising candidates for both classical and quantum communication. However, the distribution of such modes over large distances remains difficult. Intermodal coupling complicates their use with common fibers, whereas free-space transmission is thought to be strongly influenced by atmospheric turbulence. Here, we show the transmission of orbital angular momentum modes of light over a distance of 143 km between two Canary Islands, which is 50× greater than the maximum distance achieved previously. As a demonstration of the transmission quality, we use superpositions of these modes to encode a short message. At the receiver, an artificial neural network is used for distinguishing between the different twisted light superpositions. The algorithm is able to identify different mode superpositions with an accuracy of more than 80% up to the third mode order and decode the transmitted message with an error rate of 8.33%. Using our data, we estimate that the distribution of orbital angular momentum entanglement over more than 100 km of free space is feasible. Moreover, the quality of our free-space link can be further improved by the use of state-of-the-art adaptive optics systems.

Near-perfect sorting of orbital angular momentum and angular position states of light.

We present a novel method for efficient sorting of photons prepared in states of orbital angular momentum (OAM) and angular position (ANG). A log-polar optical transform is used in combination with a holographic beam-splitting method to achieve better mode discrimination and reduced cross-talk than reported previously. Simulating this method for 7 modes, we have calculated an improved mutual information of 2.43 bits/photon and 2.29 bits/photon for OAM and ANG modes respectively. In addition, we present preliminary results from an experimental implementation of this technique. This method is expected to have important applications for high-dimensional quantum key distribution systems.

Multi-photon entanglement in high dimensions

A three-photon entangled state with 3 × 3 × 2 dimensions of its orbital angular momentum is created by using two independent entangled photon pairs from two nonlinear crystals, enabling the development of a new layered quantum communication protocol. Forming the backbone of quantum technologies today, entanglement1,2 has been demonstrated in physical systems as diverse as photons3, ions4 and superconducting circuits5. Although steadily pushing the boundary of the number of particles entangled, these experiments have remained in a two-dimensional space for each particle. Here we show the experimental generation of the first multi-photon entangled state where both the number of particles and dimensions are greater than two. Two photons in our state reside in a three-dimensional space, whereas the third lives in two dimensions. This asymmetric entanglement structure6 only appears in multiparticle entangled states with d > 26. Our method relies on combining two pairs of photons, high-dimensionally entangled in their orbital angular momentum7. In addition, we show how this state enables a new type of ‘layered’ quantum communication protocol. Entangled states such as these serve as a manifestation of the complex dance of correlations that can exist within quantum mechanics.

Simulating thick atmospheric turbulence in the lab with application to orbital angular momentum communication

We describe a procedure by which a long () optical path through atmospheric turbulence can be experimentally simulated in a controlled fashion and scaled down to distances easily accessible in a laboratory setting. This procedure is then used to simulate a 1 km long free-space communication link in which information is encoded in orbital angular momentum spatial modes. We also demonstrate that standard adaptive optics methods can be used to mitigate many of the effects of thick atmospheric turbulence.