Macroscopic Quantum States Unite Bose and Cooper Pair Systems
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Guo-Jian Qiao of Graduate School of China Academy of Engineering Physics, and colleagues, have re-examined the fundamental quantization of the order parameter, termed ‘third quantization’, revealing its connection to established quantum mechanical principles. They show that this macroscopic commutation relation isn’t a new postulate but arises naturally from second quantization in large systems, offering a unifying framework for understanding both Bose-Einstein condensates and Bardeen-Cooper-Schrieffer states as macroscopic coherent states. The work proposes a new interpretation of the BCS-BEC crossover, modelling superconductivity as a transition from localised segments to a globally coherent Bose-Einstein condensate via increasing intra-segment coupling and inter-segment tunneling. Consequently, the BCS-BEC crossover phase diagram is presented as a macroscopic quantum process governed by coherent-state dynamics, providing a unified perspective on these key quantum phenomena. Quantising the order parameter reveals emergent commutation relations Second quantization is a formalism in quantum mechanics that provides a powerful method for describing many-body systems. Instead of tracking individual particles, it focuses on the collective behaviour of particle creation and annihilation operators. This approach is particularly well-suited to systems containing vast numbers of particles, such as those exhibiting Bose-Einstein condensation or superconductivity. Applying this method to such systems proved key, allowing the commutation relation, a fundamental link between the phase of the order parameter and the particle number, to emerge not as a new rule of quantum mechanics, but as a natural consequence of the behaviour of many interacting particles. This simplification of the theoretical framework is a significant advancement. The order parameter, in this context, represents a macroscopic quantum variable characterising the collective state of the system, such as the condensate wavefunction or the superconducting gap. The commutation relation mathematically expresses the inherent uncertainty in simultaneously knowing the precise phase and particle number of this order parameter. A unified description of both Bose-Einstein condensates, where bosons behave like a perfectly synchronised marching band, and Bardeen-Cooper-Schrieffer (BCS) states vital to superconductivity became possible, classifying them as macroscopic quantum states. A revisit to the quantization of the order parameter focused on the relationship between the phase and particle number of this order parameter. The commutation relation arises naturally from second quantization when considering many interacting particles, unlike the need to add new rules to quantum mechanics. The analysis used the thermodynamic limit, where the number of particles approaches infinity while the density remains constant, to model these systems, providing a mathematically tractable approximation. A superconductor was modelled as multiple segments to examine the BCS-BEC crossover; increasing intra-segment coupling drove the system from a BCS-like to a BEC-like regime, where segments behaved as macroscopic coherent states. These coherent states represent quantum states with a well-defined phase, minimising uncertainty in that variable. Inter-segment tunneling then locked the phases of these states, establishing global phase coherence and ultimately forming a bulk Bose-Einstein condensate, demonstrating the crossover as a macroscopic quantum process governed by the order parameter’s coherent-state dynamics. This modelling provides a pathway to understanding how the microscopic interactions within a superconductor can lead to macroscopic quantum phenomena. Emergent commutation relations unify Bose-Einstein condensation and superconductivity descriptions The commutation relation, linking the phase and particle number of an order parameter, emerges naturally from second quantization, resolving a long-standing need to add postulates to quantum mechanics. Previously, establishing this relation required independent assumptions about the system’s behaviour; now, it arises automatically when examining systems with many particles, simplifying theoretical models and reducing the need for ad-hoc assumptions. This refinement unifies descriptions of both Bose-Einstein condensates and Bardeen-Cooper-Schrieffer states, revealing them as macroscopic quantum states describable using bosonic coherent states, offering a new perspective on superconductivity and condensation. Coherent states are particularly useful because they closely resemble classical states, allowing for a more intuitive understanding of the macroscopic quantum behaviour. A variational approach to a Bose-Einstein condensate revealed the order parameter obeyed the Gross-Pitaevskii equation, a nonlinear partial differential equation describing the dynamics of the condensate wavefunction, with subsequent phase quantization confirming a canonical commutation relation in the thermodynamic limit. This confirms the consistency of the approach and its ability to reproduce known results for Bose-Einstein condensation. While these results unify descriptions of BEC, BCS superconductivity, and the crossover within this quantization method, they do not yet predict specific material properties or offer a clear pathway to designing room-temperature superconductors. The challenge remains to translate these theoretical insights into practical materials with enhanced superconducting properties. Some physicists have questioned whether this represents genuinely new physics, arguing it’s merely a mathematical quirk of how we describe these systems, but the behaviour arises naturally from established quantum principles, simplifying our understanding of both superconductivity and Bose-Einstein condensation. This establishes a fundamental connection between seemingly disparate areas of quantum physics, demonstrating that the behaviour of both Bose-Einstein condensates and conventional superconductors can be consistently described using the same framework. Scientists proved, by revisiting the mathematical technique, that its principles aren’t additional rules, but rather a natural consequence of established quantum mechanics when applied to systems with many interacting particles. The 01% level of accuracy achieved in the modelling further validates the approach and suggests its potential for future applications in materials science and quantum technology. The research demonstrated that the mathematical technique of third quantization isn’t a new rule of quantum mechanics, but instead arises naturally when applying standard quantum principles to systems containing many interacting particles. This finding unifies the descriptions of Bose-Einstein condensates and conventional superconductivity, suggesting both can be understood as macroscopic quantum states described by coherent states. By modelling a superconductor as an assembly of segments, researchers showed how the system transitions between BCS-like and BEC-like behaviour as coupling increases. The modelling achieved 0.1% accuracy, validating the approach and offering a consistent framework for understanding these quantum phenomena. 👉 More information🗞 Third Quantization for Order Parameter (I): BCS-BEC crossover with macroscopically coherent state🧠 ArXiv: https://arxiv.org/abs/2604.21288 Tags: