# Research

## Energy and charge transport

### Exciton transport in photosynthesis

Photosynthetic organisms harvest light using large antenna complexes containing many chlorophyll molecules. The energy harvested by the antennas is then transported to the reaction centres, where the first chemical steps occur. Recent experiments have suggested that, surprisingly, the excitation energy can be transported in a coherent, wavelike manner. It was previously doubted that quantum effects could survive for so long in biological systems at room temperature.

We recently clarified the relationship between these experimental observations—carried out with pulsed lasers—and the behaviour of the complexes in incoherent natural light. In sunlight, energy transport occurs at steady state, meaning that the wavelike dynamics observed experimentally is, in a sense, an experimental artefact. However, we also identified mechanisms by which quantum effects *can* enhance light harvesting even in incoherent light, and we are currently working on applying those findings to the design of artificial light-harvesting systems.

- Geometry, supertransfer, and optimality in the light harvesting of purple bacteriaThe remarkable rotational symmetry of the photosynthetic antenna complexes of purple bacteria has long been thought to enhance their light harvesting and excitation energy transport. We study the role of symmetry by modeling hypothetical antennas whose symmetry is broken by altering the orientations of the bacteriochlorophyll pigments. We find that in both LH2 and LH1 complexes, symmetry increases energy transfer rates by enabling the cooperative, coherent process of supertransfer. The enhancement is particularly pronounced in the LH1 complex, whose natural geometry outperforms the average randomized geometry by 5.5 standard deviations, the most significant coherence-related enhancement found in a photosynthetic complex.
- Distinguishing the roles of energy funnelling and delocalization in photosynthetic light harvestingPhotosynthetic complexes improve the transfer of excitation energy from peripheral antennas to reaction centers in several ways. In particular, a downward energy funnel can direct excitons in the right direction, while coherent excitonic delocalization can enhance transfer rates through the cooperative phenomenon of supertransfer. However, isolating the role of purely coherent effects is difficult because any change to the delocalization also changes the energy landscape. Here, we show that the relative importance of the two processes can be determined by comparing the natural light-harvesting apparatus with counterfactual models in which the delocalization and the energy landscape are altered. Applied to the example of purple bacteria, our approach shows that although supertransfer does enhance the rates somewhat, the energetic funnelling plays the decisive role. Because delocalization has a minor role (and is sometimes detrimental), it is most likely not adaptive, being a side-effect of the dense chlorophyll packing that evolved to increase light absorption per reaction center.
- Benchmarking calculations of excitonic couplings between bacteriochlorophyllsExcitonic couplings between (bacterio)chlorophyll molecules are necessary for simulating energy transport in photosynthetic complexes. Many techniques for calculating the couplings are in use, from the simple (but inaccurate) point-dipole approximation to fully quantum-chemical methods. We compared several approximations to determine their range of applicability, noting that the propagation of experimental uncertainties poses a fundamental limit on the achievable accuracy. In particular, the uncertainty in crystallographic coordinates yields an uncertainty of about 20% in the calculated couplings. Because quantum- chemical corrections are smaller than 20% in most biologically relevant cases, their considerable computational cost is rarely justified. We therefore recommend the electrostatic TrEsp method across the entire range of molecular separations and orientations because its cost is minimal and it generally agrees with quantum-chemical calculations to better than the geometric uncertainty. Understanding these uncertainties can guard against striving for unrealistic precision; at the same time, detailed benchmarks can allow important qualitative questions—which do not depend on the precise values of the simulation parameters—to be addressed with greater confidence about the conclusions..
- Importance of excitation and trapping conditions in photosynthetic environment-assisted energy transportIt has been argued that excitonic energy transport in photosynthetic complexes is efficient because of a balance between coherent evolution and decoherence, a phenomenon called environment-assisted quantum transport (ENAQT). Studies of ENAQT have usually assumed that the excitation is initially localized on a particular chromophore, and that it is transferred to a reaction center through a similarly localized trap. However, these assumptions are not physically accurate. We show that more realistic models of excitation and trapping can lead to very different predictions about the importance of ENAQT. In particular, although ENAQT is a robust effect if one assumes a localized trap, its effect can be negligible if the trapping is more accurately modeled as Forster transfer to a reaction center. Our results call into question the suggested role of ENAQT in the photosynthetic process of green sulfur bacteria and highlight the subtleties associated with drawing lessons for designing biomimetic light-harvesting complexes.
- Does coherence enhance transport in photosynthesis?Recent observations of coherence in photosynthetic complexes have led to the question of whether quantum effects can occur , not under femtosecond laser pulses but in incoherent sunlight and at steady state, and, if so, whether the coherence explains the high exciton transfer efficiency. We distinguish several types of coherence and show that although some photosynthetic pathways are partially coherent processes, photosynthesis in nature proceeds through stationary states. This distinction allows us to rule out several mechanisms of transport enhancement in sunlight. In particular, although they are crucial for understanding exciton transport, neither wavelike motion nor microscopic coherence, on their own, enhance the efficiency. By contrast, two partially coherent mechanisms—ENAQT and supertransfer—can enhance transport even in sunlight and thus constitute motifs for the optimisation of artificial sunlight harvesting. Finally, we clarify the importance of ultrafast spectroscopy in understanding incoherent processes.
- Environment-assisted quantum transportTransport phenomena at the nanoscale are of interest due to the presence of both quantum and classical behavior. In this work, we demonstrate that quantum transport efficiency can be enhanced by a dynamical interplay of the system Hamiltonian with pure dephasing induced by a fluctuating environment. This is in contrast to fully coherent hopping that leads to localization in disordered systems, and to highly incoherent transfer that is eventually suppressed by the quantum Zeno effect. We study these phenomena in the Fenna–Matthews–Olson protein complex as a prototype for larger photosynthetic energy transfer systems. We also show that the disordered binary tree structures exhibit enhanced transport in the presence of dephasing.

### Photophysics of organic photovoltaics

Organic solar cells differ from conventional inorganic ones not only in their flexibility, but also in their fundamental physics. Organic materials are disordered, meaning that charges tend to be localised and move by hopping, unlike the band transport in inorganic devices. In addition, the localisation of the electron and the hole increases their Coulomb attraction, making it harder to separate them and produce an electric current.

It is still unclear exactly how the charges overcome their considerable electrostatic attraction, sometimes with an efficiency approaching 100%. We are working to understand the fundamental photophysics involved, often in close collaboration with experimentalists.

- Intercalated vs nonintercalated morphologies in donor−acceptor bulk heterojunction solar cells: PBTTT:fullerene charge generation and recombination revisitedIn this Letter, we study the role of the donor:acceptor interface nanostructure upon charge separation and recombination in organic photovoltaic devices and blend films, using mixtures of PBTTT and two different fullerene derivatives (PC70BM and ICTA) as models for intercalated and nonintercalated morphologies, respectively. Thermodynamic simulations show that while the completely intercalated system exhibits a large free-energy barrier for charge separation, this barrier is significantly lower in the nonintercalated system and almost vanishes when energetic disorder is included in the model. Despite these differences, both femtosecond-resolved transient absorption spectroscopy (TAS) and time-delayed collection field (TDCF) exhibit extensive first-order losses in both systems, suggesting that geminate pairs are the primary product of photoexcitation. In contrast, the system that comprises a combination of fully intercalated polymer:fullerene areas and fullerene-aggregated domains (1:4 PBTTT:PC70BM) is the only one that shows slow, second-order recombination of free charges, resulting in devices with an overall higher short-circuit current and fill factor. This study therefore provides a novel consideration of the role of the interfacial nanostructure and the nature of bound charges and their impact upon charge generation and recombination.
- Electric field and mobility dependent first-order recombination losses in organic solar cellsThe origin of photocurrent losses in the power-generating regime of organic solar cells (OSCs) remains a controversial topic, although recent literature suggests that the competition between bimolecular recombination and charge extraction determines the bias dependence of the photocurrent. Here the steady-state recombination dynamics is studied in bulk-heterojunction OSCs with different hole mobilities from short-circuit to maximum power point. It is shown that in this regime, in contrast to previous transient extracted charge and absorption spectroscopy studies, first-order recombination outweighs bimolecular recombination of photogenerated charge carriers. This study demonstrates that the first-order losses increase with decreasing slower carrier mobility, and attributes them to either mobilization of charges trapped at the donor:acceptor interface through the Poole–Frenkel effect, and/or recombination of photogenerated and injected charges. The dependence of both first-order and higher-order losses on the slower carrier mobility explains why the field dependence of OSC efficiencies has historically been attributed to charge-extraction losses.
- Entropy and disorder enable charge separation in organic solar cellsAlthough organic heterojunctions can separate charges with near-unity efficiency and on a sub-picosecond timescale, the full details of the charge-separation process remain unclear. In typical models, the Coulomb binding between the electron and the hole can exceed the thermal energy kT by an order of magnitude, making it impossible for the charges to separate before recombining. Here, we consider the entropic contribution to charge separation in the presence of disorder and find that even modest amounts of disorder have a decisive effect, reducing the charge-separation barrier to about kT or eliminating it altogether. Therefore, the charges are usually not thermodynamically bound at all and could separate spontaneously if the kinetics otherwise allowed it. Our conclusion holds despite the worst-case assumption of localised, thermalised carriers, and is only strengthened if mechanisms like delocalisation or 'hot' states are also present.
- Slower carriers limit charge generation in organic semiconductor light-harvesting systemsBlends of electron-donating and -accepting organic semiconductors are widely used as photoactive materials in next-generation solar cells and photodetectors. The yield of free charges in these systems is often determined by the separation of interfacial electron–hole pairs, which is expected to depend on the ability of the faster carrier to escape the Coulomb potential. Here we show, by measuring geminate and non-geminate losses and key transport parameters in a series of bulk-heterojunction solar cells, that the charge-generation yield increases with increasing slower carrier mobility. This is in direct contrast with the well-established Braun model where the dissociation rate is proportional to the mobility sum, and recent models that underscore the importance of fullerene aggregation for coherent electron propagation. The behaviour is attributed to the restriction of opposite charges to different phases, and to an entropic contribution that favours the joint separation of both charge carriers.
- Spectral dependence of the internal quantum efficiency of organic solar cells: Effect of charge generation pathwaysThe conventional picture of photocurrent generation in organic solar cells involves photoexcitation of the electron donor, followed by electron transfer to the acceptor via an interfacial charge-transfer state (Channel I). It has been shown that the mirror-image process of acceptor photoexcitation leading to hole transfer to the donor is also an efficient means to generate photocurrent (Channel II). The donor and acceptor components may have overlapping or distinct absorption characteristics. Hence, different excitation wavelengths may preferentially activate one channel or the other, or indeed both. As such, the internal quantum efficiency (IQE) of the solar cell may likewise depend on the excitation wavelength. We show that several model high-efficiency organic solar cell blends, notably PCDTBT:PC70BM and PCPDTBT:PC60/70BM, exhibit flat IQEs across the visible spectrum, suggesting that charge generation is occurring either via a dominant single channel or via both channels but with comparable efficiencies. In contrast, blends of the narrow optical gap copolymer DPP-DTT with PC70BM show two distinct spectrally flat regions in their IQEs, consistent with the two channels operating at different efficiencies. The observed energy dependence of the IQE can be successfully modeled as two parallel photodiodes, each with its own energetics and exciton dynamics but both having the same extraction efficiency. Hence, an excitation-energy dependence of the IQE in this case can be explained as the interplay between two photocurrent-generating channels, without recourse to hot excitons or other exotic processes.

## Quantum computing and quantum simulation

### Photonic quantum computing and simulation

Photons are promising candidates for quantum communication and computation because they are easily isolated from noise, retaining their quantum correlations as long as they are not absorbed. The ability to control them precisely has allowed us—in collaboration with experimental groups such as the UQ Quantum Technology Laboratory—to build simulators of quantum phenomena, such as topologically protected bound states, that have not yet been directly observed in nature.

Although the stability of photons is essential for quantum communication, it also makes it challenging to simulate quantum systems subject to environmental noise. We have developed several techniques for adding controllable amounts of decoherence to photonic circuits, allowing us to demonstrate effects such as environment-assisted quantum transport, which we previously described in the context of photosynthetic energy transport.

- Enhancing quantum transport in a photonic network using controllable decoherenceTransport phenomena on a quantum scale appear in a variety of systems, ranging from photosynthetic complexes to engineered quantum devices. It has been predicted that the efficiency of coherent transport can be enhanced through dynamic interaction between the system and a noisy environment. We report an experimental simulation of environment-assisted coherent transport, using an engineered network of laser-written waveguides, with relative energies and inter-waveguide couplings tailored to yield the desired Hamiltonian. Controllable-strength decoherence is simulated by broadening the bandwidth of the input illumination, yielding a significant increase in transport efficiency relative to the narrowband case. We show integrated optics to be suitable for simulating specific target Hamiltonians as well as open quantum systems with controllable loss and decoherence.
- A two-qubit photonic quantum processor and its application to solving systems of linear equationsLarge-scale quantum computers will require the ability to apply long sequences of entangling gates to many qubits. In a photonic architecture, where single-qubit gates can be performed easily and precisely, the application of consecutive two-qubit entangling gates has been a significant obstacle. Here, we demonstrate a two-qubit photonic quantum processor that implements two consecutive CNOT gates on the same pair of polarisation-encoded qubits. To demonstrate the flexibility of our system, we implement various instances of the quantum algorithm for solving of systems of linear equations.
- Observation of topologically protected bound states in a one-dimensional photonic systemTopological phases exhibit some of the most striking phenomena in modern physics. Much of the rich behaviour of quantum Hall systems, topological insulators, and topological superconductors can be traced to the existence of robust bound states at interfaces between different topological phases. This robustness has applications in metrology and holds promise for future uses in quantum computing. Engineered quantum systems—notably in photonics, where wavefunctions can be observed directly—provide versatile platforms for creating and probing a variety of topological phases. Here we use photonic quantum walks to observe bound states between systems with different bulk topological properties and demonstrate their robustness to perturbations—a signature of topological protection. Although such bound states are usually discussed for static (time-independent) systems, here we demonstrate their existence in an explicitly time-dependent situation. Moreover, we discover a new phenomenon: a topologically protected pair of bound states unique to periodically driven systems.
- Discrete single-photon quantum walks with tunable decoherenceQuantum walks have a host of applications, ranging from quantum computing to the simulation of biological systems. We present an intrinsically stable, deterministic implementation of discrete quantum walks with single photons in space. The number of optical elements required scales linearly with the number of steps. We measure walks with up to 6 steps and explore the quantum-to-classical transition by introducing tunable decoherence. Finally, we also investigate the effect of absorbing boundaries and show that decoherence significantly affects the probability of absorption.

### Quantum computing for chemistry

Quantum calculations of chemical and physical properties, such as molecular energies or reaction rates, increase in difficulty with the size of the system, sometimes exponentially fast. As a result, the most accurate techniques are restricted to small systems. The fundamental obstacle is the presence of entanglement (correlation), which is difficult to represent efficiently on a classical computer.

We have shown that quantum computers could circumvent this problem in a natural way, by using a controllable quantum process to run a simulation of the unknown process. We have developed a suite of quantum methods for chemical problems, including the simulation of chemical reactions and the determination of properties like the dipole moment. Our proposals have been implemented experimentally on small scales, and we continue to collaborate with experimentalists on pushing the limits of quantum simulation.

- Simulating chemistry using quantum computersThe difficulty of simulating quantum systems, well known to quantum chemists, prompted the idea of quantum computation. One can avoid the steep scaling associated with the exact simulation of increasingly large quantum systems on conventional computers, by mapping the quantum system to another, more controllable one. In this review, we discuss to what extent the ideas in quantum computation, now a well-established field, have been applied to chemical problems. We describe algorithms that achieve significant advantages for the electronic-structure problem, the simulation of chemical dynamics, protein folding, and other tasks. Although theory is still ahead of experiment, we outline recent advances that have led to the first chemical calculations on small quantum information processors.
- Towards quantum chemistry on a quantum computerExact first-principles calculations of molecular properties are currently intractable because their computational cost grows exponentially with both the number of atoms and basis set size. A solution is to move to a radically different model of computing by building a quantum computer, which is a device that uses quantum systems themselves to store and process data. Here we report the application of the latest photonic quantum computer technology to calculate properties of the smallest molecular system: the hydrogen molecule in a minimal basis. We calculate the complete energy spectrum to 20 bits of precision and discuss how the technique can be expanded to solve large-scale chemical problems that lie beyond the reach of modern supercomputers. These results represent an early practical step toward a powerful tool with a broad range of quantum-chemical applications.
- Quantum algorithm for molecular properties and geometry optimizationQuantum computers, if available, could substantially accelerate quantum simulations. We extend this result to show that the computation of molecular properties (energy derivatives) could also be sped up using quantum computers. We provide a quantum algorithm for the numerical evaluation of molecular properties, whose time cost is a constant multiple of the time needed to compute the molecular energy, regardless of the size of the system. Molecular properties computed with the proposed approach could also be used for the optimization of molecular geometries or other properties. For that purpose, we discuss the benefits of quantum techniques for Newton’s method and Householder methods. Finally, global minima for the proposed optimizations can be found using the quantum basin hopper algorithm, which offers an additional quadratic reduction in cost over classical multi-start techniques.
- Polynomial-time quantum algorithm for the simulation of chemical dynamicsThe computational cost of exact methods for quantum simulation using classical computers grows exponentially with system size. As a consequence, these techniques can be applied only to small systems. By contrast, we demonstrate that quantum computers could exactly simulate chemical reactions in polynomial time. Our algorithm uses the split-operator approach and explicitly simulates all electron-nuclear and interelectronic interactions in quadratic time. Surprisingly, this treatment is not only more accurate than the Born–Oppenheimer approximation but faster and more efficient as well, for all reactions with more than about four atoms. This is the case even though the entire electronic wave function is propagated on a grid with appropriately short time steps. Although the preparation and measurement of arbitrary states on a quantum computer is inefficient, here we demonstrate how to prepare states of chemical interest efficiently. We also show how to efficiently obtain chemically relevant observables, such as state-to-state transition probabilities and thermal reaction rates. Quantum computers using these techniques could outperform current classical computers with 100 qubits.