Magnetic semiconductors We saw last time that: We d like to do spintronics in semiconductors, because semiconductors have many nice properties (gateability, controllable spin-orbit effects, long spin lifetimes). Injecting spin efficiently into semiconductors from FM metals is hard because of the conductivity mismatch between materials, and the best way to do it is with tunnel barriers. Ideally, want FM semiconductors: Ohno et al., Nature 402 790 (1999) (Dilute) Magnetic semiconductors Getting FM in semiconductors is not trivial. Recall why we have FM in metals: Band structure leads to enhanced exchange interactions between (relatively) localized spins (d- or f-shell electrons). Conduction electrons can play a very important role. In semiconductors, Carriers present are only there because of doping, and at much lower concentrations. No natural localized spins. Situation today: Add localized spins by doping (e.g. with Mn). Mechanism of FM still not universally clear. Curie temperatures still not great 1
Magnetic semiconductors - description Main family: III-V compound semiconductors. Most common magnetic dopant in Mn (group II). Result: III(Mn)-V compounds are p-type. Grown by low-temperature MBE - not thermodynamically stable. Typical concentration something like Ga 0.95 Mn 0.05 As. Ohno et al., Science 281 951 (1998) Note that these materials are quite heavily doped! II-VI materials have been much harder to work with (unable to dope; exchange interaction difficult to control). Magnetic semiconductors - description Tanaka., J. Cryst. Growth 278, 25 (2005) 2
DMS: magnetic properties Koshihara et al., PRL 78, 4617 (1997). In 0.95 Mn 0.05 As has T c ~ 30 K. Ga 0.95 Mn 0.05 As has T c ~ 110 K. Magnetic order depends very strongly on carrier density! Can therefore be manipulated. Light-induced ferromagnetism! DMS: magnetic properties Sensitivity to carrier concentration means it s possible to have gateable ferromagnetism! Potentially very exciting for spintronics applications. Major problems: Temperature range is poor. Materials compatibility is not very good, either. Ohno et al., Nature 408 944 (2000) 3
DMS: heterostructures Can try to avoid disorder problems by modulation doping, as in regular heterostructures. So far, have increased T c up to higher values (~ 175 K) in GaMnAs system. Tanaka., J. Cryst. Growth 278, 25 (2005) DMS: group IV possibilities Recent progress in Mn x Ge 1-x growth. Again, low T ferromagnetism, with gate modulation as hole concentration is varied. Park et al., Science 295 651 (2002) 4
Quantum Computation - a very quick intro A prime motivation for manipulation of spins in semiconductors is to perform quantum information processsing. What is quantum computation? Using the quantum properties of quantum-bits (qubits) to perform calculations more rapidly (in principle) than is possible with classical computers. Why should this be possible? Imagine a collection of N bits that can be 1 or 0. With these N bits one can represent any integer from 0 up to 2 N -1. Now suppose these bits are quantum mechanical objects. http://qist.lanl.gov/ = New Roadmap for QIP. Qubits and their properties Consider N spin-1/2 particles, with spin up corresponding to 1 and spin down corresponding to 0. The quantum mechanical state of these states for 1 such qubit is written 1> or 0>. 1 Now, though, we can consider superpositions: ( 0 + 1 ) 2 More conventional to think of these spins as column vectors: 0 1 0 1 0 1 0 + 1 1/ 2 1 ( ) 2 1/ 2 Logic operations are now actually unitary operations on the spins (though in general this requires a dial-a-hamiltonian box). 5
Qubits and their properties A generic unitary operator: U θ cos( θ / 2) sin( θ / 2) sin( θ / 2) cos( θ / 2) So, U π inverts a qubit (up to a phase): U π 0 = 1 1 0 0 1 0 1 0 1 1 0 Uπ 0 = = = 1 U 0 1 0 1 0 π 1 = = = 1 0 0 1 So, U π/2 produces a superposition: U π ( 0 1 ) 1 / 2 0 = + 2 What can this do for us? Imagine a string of N qubits, starting out in 0000 >. Use the state of each qubit to represent a binary number, a. Now apply the linear operator U π/2 to each qubit in this state. Result: 1 1 N a N 2 a= 0 We ve now prepared the qubits in a superposition of all their possible values! From a linear number of operations N, we ve produced a superposition with an exponentially large number of terms, 2 N. 6
What can this do for us? Now suppose we had two such strings. Suppose we had an operator O that, when operating on a string a returned a particular function f(a). That is, O a; 0 a; f ( a) Consider applying this operator to our big superposition: O 1 2 N 1 N a= 0 a;0 1 2 N 1 N a= 0 a; f ( a) Now with a single operation we ve computed f(a) for an exponentially large number of possible a. That s the crux of quantum computation! Because of this kind of quantum parallelism, it s possible to do certain computations much faster than with classical computers. What kinds of applications? There are already quantum algorithms (well-defined series of operations) for: Searching databases (Lov Grover) Factoring large numbers (Peter Schor) This is an extremely hot field in computer science right now. Big funding: DARPA, NSA Big players: IBM, Microsoft, Intel 7
What do we need to accomplish all this? Requirements according to David DiVincenzo (IBM): 1. Be a scalable physical system with well-defined qubits 2. Be initializable to a simple fiducial state such as 000...> 3. Have much longer decoherence times 4. Have a universal set of quantum gates 5. Permit high quantum efficiency, qubit-specific measurements Universal quantum gates: can be proven that one only needs two kinds of gates (NOT and XOR) operating on 2 qubits at a time to do general quantum computations (with some other subtleties). Why is this difficult? One needs to be able to go in and couple qubits together with great precision, almost aribitrarily. How can one manipulate one particular qubit without accidently decohering the entire system? System must be isolated from the environment so that coherence times are long compared to operation times. One really wants to do this in a way that s scaleable. 8
How are people trying to implement QIP? Several approaches: Optical trapping / manipulation of atoms and ions NMR (liquid, solids) Quantum dots Superconducting qubits Everyone would love to do this in the solid state, because it would scale well and interface with existing technology. NMR Idea is to use nuclear spins in some system as qubits. Problem: you don t really have pure quantum states. Solution: with 10 22 qubits, you can fudge things and have effective pure states. Ex: investigators at MIT have used 13 nuclear spins in a molecule to factor the number 15 = 5 x 3. NMR in molecules does not scale well: Individual chemical shifts of NMR frequencies are too limited - can t individually flip 8456th spin out of 10000, for example. 9
NMR hybrid - solid state possibility Kane., Nature 393 133 (1998) Use P dopants in Si as qubits. Big hyperfine + Starck effects = dialable NMR frequencies to address individual qubits. Could be read out electrostatically. Quantum dots Idea of Divincenzo and Loss: use electron spins as qubits. Each qubit is a single electron in a quantum dot. Use gates to manipulate exchange interaction between neighboring qubits. Use SETs to read out states of qubits when done. Univ. of Wisconsin 10
Quantum dots Hanson et al., PRL 94, 196802 (2005) Possible to read out spin states of single electrons in quantum dots! Energies and wavefunctions of different spin states can differ. Quantum dots Hanson et al., PRL 94, 196802 (2005) Possible to read out spin states of single electrons in quantum dots! Energies and wavefunctions of different spin states can differ. 11
Quantum dots Petta et al., Science 309, 2180 (2005) Possible to read out spin states of single electrons in quantum dots! Can do manipulations at high speeds. Quantum dots Petta et al., Science 309, 2180 (2005) Possible to read out spin states of single electrons in quantum dots! Can do manipulations at high speeds. 12
Superconducting qubits Physics Today, November 2005 Several groups trying to use superconducting structures as qubits. Possible qubits include charge based ( Cooper pair box ), fluxbased, and Josephson phase based. Readout, manipulation all use nanofab. SQUIDs and SETs. Superconducting qubits McDermott et al., Science 307, 1299 (2005) 13
Ion trap qubits Recent advances suggest that ion traps may actually work very well! Leibfried et al., Nature 438, 639 (2005) Ion trap qubits Haffner et al., Nature 438, 643 (2005) 14
QIP summary: Very intriguing ideas Number of possible technologies, but it s not clear if any of them will work well in a practical manner. Many implementations would depend critically on nanofabrication and nanotechnology. Progress has been much more rapid than I imagined two years ago, particularly in the superconducting qubits and semiconductor quantum dot approaches. 15