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Quantum states Ch. 13.3 • A quantum state corresponds to a specific wave packet (= wave function). • A quantum state is characterized by a set of quantum numbers, such as the energy E. • Quantum numbers can be measured exactly. For example, the uncertainty E is zero for a stable state, where one can take an infinite time t for measuring the energy. Strange effects involving quantum states • Quantum ‘jump’: During the transition from one quantum state to another, the wave packet morphs continuously. • Superposition: One particle is in two quantum states at the same time. • Entanglement: Two particles in two quantum states can become intertwined inseparably. This occurs for electrons, photons, or any quantum object. Two quantum states Superposition state • During a quantum jump an electron morphs from one wave packet into another (shown in three dimensions). • While it is morphing, an electron is in a superposition state. A superposition state (1 particle, 2 states) Dirac bracket, designating a state • Margarita or beer? • This superposition state (of mind) gives equal probabilities to choosing margarita or beer. • The actual outcome is not determined until the experiment is performed (in a bar). • The question arises whether our brain makes such quantum decisions. Is that “free will ” ? How do we make decisions ? What is going on in our brain ? A. Classical physics: Every decision we ever make is determined in advance, but we don’t know it. B. Quantum physics: Decisions are unpredictable. C. Complexity: The brain is not a quantum system. It contains 100 billion neurons, and each neuron by itself is too large to be a quantum system. A new branch of physics is searching for simple laws of complex systems (such as the Santa Fe Institute). How do primitive ants build a complex ant nest (next slide). Each of them obeys simple rules, like a neuron. Leaf cutter ants Cast of an ant nest School of fish avoiding a sea lion An entangled state (2 particles, 2 states) It takes more than one particle (person) to become entangled. You Your buddy • You and your buddy are hitting a bar. • Both of you have a hard time deciding what to order. • Eventually you decide for beer. • Your buddy follows suit. • Had you decided for margarita, your buddy would have ordered margarita as well. Another entangled state • Two contrarians are hitting a bar. • Both have a hard time deciding what to order. • Eventually one of them decides for beer. • The other orders …? Quantum nonlocality: Spooky action at a distance Two entangled particles cannot be separated, even after they leave the interaction zone , where they became entangled. They act as a single object. Thus, they appear in two different places at the same time. Fig. 14.10 Manipulating one of the entangled wave packets affects the other. Quantum computing (optional) • A normal computer uses at bit which is either 0 or 1 . • A qubit (quantum bit) is a superposition of 2 quantum states. • A quantum computer is good at cracking codes (= factoring large numbers) and at searching large data bases. • In practice, the most sophisticated calculation performed so far is 21 = 3 7 . • But there has been enormous progress in creating complex quantum states which Schrödinger and Einstein could only ponder theoretically. qubits • Take two states of an electron, labeled |0 and |1 • Superposition of 2 states of 1 electron: |0 + |1 = 1 qubit • Superposition of 4 states of 2 electrons: |0,0 + |1,1 + |1,0 + |0,1 = 2 qbits • Superposition of 2n states of n electrons: = n qubits Each of the quantum states |.. has a certain probability as pre-factor, which is omitted here. Many qubits are very powerful • A normal computer can process only 1 combination of n bits (typically 64 bits). • A quantum computer processes all 2n combinations of two states at the same time. This corresponds to a normal computer with 2n processors. • Processing 64 qubits instead of 64 bits increases the speed by a factor of 264 = 2 · 1019 = 20000000000000000000 A a single-electron trap for a qubit The electron is captured between the four electrodes. The current IQPC senses whether an electron is in the trap.